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Algebraic objects generated by topological structure. (English. Russian original) Zbl 0665.22001

J. Sov. Math. 45, No. 1, 956-990 (1989); translation from Itogi Nauki Tekh., Ser. Algebra, Topologiya, Geom. 25, 141-198 (1987).
See the review in Zbl 0631.22001.

MSC:

22A05 Structure of general topological groups
54C40 Algebraic properties of function spaces in general topology
54H15 Transformation groups and semigroups (topological aspects)
22-02 Research exposition (monographs, survey articles) pertaining to topological groups

Citations:

Zbl 0631.22001
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Full Text: DOI

References:

[1] A. V. Arkhangel’skii, ?On mappings connected with topological groups,? Dokl. AN SSSR,181, No. 6, 1303?1306 (1968).
[2] A. V. Arkhangel’skii, Topological Spaces and Continuous Mappings. Notes on Topological Groups [in Russian], Moscow State Univ. (1969).
[3] A. V. Arkhangel’skii, ?On some topological spaces occurring in functional analysis,? Usp. Mat. Nauk,31, No. 5, 17?32 (1976).
[4] A. V. Arkhangel’skii, ?On continuous function spaces in the topology of pointwise convergence,? Dokl. AN SSSR,240, No. 3, 505?508 (1978).
[5] A. V. Arkhangel’skii, ?Structure and classification of topological spaces and cardinal invariants,? Usp. Mat. Nauk,33, No. 6, 29?84 (1978).
[6] A. V. Arkhangel’skii, ?Cardinal invariants of topological groups. Embeddings and condensations,? Dokl. AN SSSR,247, No. 4, 779?782 (1979).
[7] A. V. Arkhangel’skii, ?The frequency spectrum of a topological space and the product operation,? Tr. Mosk. Mat. Obshch.,40, 171?206 (1979).
[8] A. V. Arkhangel’skii, ?On relations between the invariants of topological groups and their subspaces,? Usp. Mat. Nauk,35, No. 3, 3?22 (1980).
[9] A. V. Arkhangel’skii, ?The principle of ?-approximation and the criterion of equal dimension for bicompacta,? Dokl. AN SSSR,252, No. 4, 777?780 (1980).
[10] A. V. Arkhangel’skii, Supplement to J. L. Kelly, General Topology [Russian translation], Nauka, Moscow (1981), pp. 365?409.
[11] A. V. Arkhangel’skii, ?Classes of topological groups,? Usp. Mat. Nauk,36, No. 3, 127?146 (1981).
[12] A. V. Arkhangel’skii, ?Every topological group is a factor-group of a zero-dimensional topological group,? Dokl. AN SSSR,258, No. 5, 1037?1040 (1981).
[13] A. V. Arkhangel’skii, ?On linear homeomorphisms of function spaces,? Dokl. AN SSSR,264, No. 6, 1289?1292 (1982).
[14] A. V. Arkhangel’skii, ?The theorem of ?-approximation and functional duality,? Mat. Zametki,31, No. 3, 421?432 (1982).
[15] A. V. Arkhangel’skii, ?Factorization theorems and function spaces: stability and monolithicity,? Dokl. AN SSSR,265, No. 5, 1039?1043 (1982).
[16] A. V. Arkhangel’skii, ?Function spaces and completeness type conditions,? Vestn. Mosk. Gos. Univ., Mat., Mekh., No. 6, 4?9 (1983).
[17] A. V. Arkhangel’skii, ?Topological properties of function spaces: duality theorems,? Dokl. AN SSSR,269, No. 6, 1289?1292 (1983).
[18] A. V. Arkhangel’skii, ?Function spaces in the topology of pointwise convergence and compacta,? Usp. Mat. Nauk,39, No. 5, 11?50 (1984).
[19] A. V. Arkhangel’skii, ?Continuous mappings, factorization theorems and function spaces,? Trudy Mosk. Mat. Obshch.,47, 3?21 (1984).
[20] A. V. Arkhangel’skii, ?Function spaces in the topology of pointwise convergence, Part 1,? in: General Topology: Function Spaces and Dimension [in Russian], Moscow (1985), pp. 3?66.
[21] A. V. Arkhangel’skii, ?Hurewicz spaces, analytical sets and fan tightness of function spaces,? Dokl. AN SSSR,287, No. 3, 525?528 (1986).
[22] A. V. Arkhangel’skii, ?Continuous images of Lindelöf ?-groups, Dokl. AN SSSR,265, No. 10 (1987).
[23] A. V. Arkhangel’skii, ?Topological homogeneity. Topological groups and their continuous images,? Usp. Mat. Nauk,42, No. 2, 69?105 (1987).
[24] A. V. Arkhangel’skii and V. I. Ponomarev, Elements of General Topology through Problems and Exercises [in Russian], Nauka, Moscow (1974).
[25] A. V. Arkhangel’skii and V. V. Tkachuk, Function Spaces and Topological Invariants [in Russian], Moscow State Univ., (1985).
[26] M. O. Asanov, ?On cardinal invariants of continuous function spaces,? in: Modern Topology and Set Theory [in Russian], Izhevsk, No. 2 (1979), pp. 8?12.
[27] M. O. Asanov, ?On spaces of continuous mappings,? Izv. Vuzov, Mat., No. 4, 6?10 (1980).
[28] M. O. Asanov and N. V. Velichko, ?Compact sets in Cp(X),? Comment. Math. Univ. Carol.,22, No. 2, 255?266 (1981). · Zbl 0491.54011
[29] V. K. Bel’nov, ?Some theorems on free abelian metrizable groups,? Sib. Mat. Zh.,13, 1213?1228 (1972).
[30] V. K. Bel’nov, ?On free abelian metrizable groups,? Dokl. AN SSSR,202, No. 4, 743?746 (1972).
[31] V. K. Bel’nov, ?The dimension of topologically homogeneous spaces and free homogeneous spaces,? Dokl. AN SSSR,238, No. 4, 781?784 (1978).
[32] V. K. Bel’nov, ?On the dimension of free topological groups,? 4th Tiraspol’ Symp. on General Topology and Its Applications [in Russian], Kishinev (1979), p. 182.
[33] Yu. Kh. Bregman, ?On lacy topological groups,? in: Topological Spaces and Their Mappings [in Russian], Riga (1983), pp. 3?9.
[34] M. S. Burgin, ?Topological algebras with continuous systems of operations,? Dokl. AN SSSR,213, No. 3, 505?508 (1973). · Zbl 0293.08003
[35] Yu. A. Burov, ?On properties of (weakly)l-equivalent spaces,? in: General Topology. Mappings of Topological Spaces [in Russian], Moscow State Univ. (1986), pp. 13?19.
[36] A. Weyl, Integration in Topological Groups and Its Applications [Russian translation], IL, Moscow (1950).
[37] N. V. Velichko, ?On weak topology of continuous function spaces,? Mat. Zametki,30, No. 5, 703?712 (1981). · Zbl 0505.54016
[38] N. V. Velichko, ?On the theory of continuous function spaces,? Usp. Mat. Nauk,37, No. 4, 149?150 (1982). · Zbl 0527.54013
[39] E. M. Vechtomov, ?Isomorphism of multiplicative semigroups of continuous function rings,? Sib. Mat. Zh.,19, No. 4, 759?771 (1978). · Zbl 0428.54009
[40] M. I. Graev, ?Free topological groups,? Izv. AN SSSR, Ser. Mat.,12, No. 3, 279?324 (1948).
[41] M. I. Graev, ?The theory of topological groups, I,? Usp. Mat. Nauk,5, No. 2, 3?56 (1950).
[42] S. P. Gul’ko, ?On properties of sets lying in ?-products,? Dokl. AN SSSR,237, No. 3, 505?507 (1977).
[43] S. P. Gul’ko, ?On properties of some function spaces,? Dokl. AN SSSR,243, No. 4, 839?842 (1978).
[44] S. P. Gul’ko, ?On the structure of continuous function spaces and their hereditary paracompactness,? Usp. Mat. Nauk,34, No. 6, 33?40 (1979).
[45] S. P. Gul’ko, ?On properties of function space,? Seminar on General Topology [in Russian], Moscow State Univ. (1981), pp. 8?41.
[46] S. P. Gul’ko and A. V. Os’kin, ?Isomorphic classification of continuous function spaces on completely ordered bicompacta,? Funkts. Anal. Prilozhen.,9, No. 1, 61?612 (1975). · Zbl 0315.35072 · doi:10.1007/BF01078183
[47] S. P. Gul’ko and T. E. Khmyleva, ?Compactness is not preserved by t-equivalence relation,? Mat. Zametki,39, No. 6, 895?903 (1986). · Zbl 0629.54007
[48] I. I. Guran, ?On topological groups close to finally compact,? Dokl. AN SSSR,256, No. 6, 1305?1307 (1981).
[49] T. I. Guran, ?Topology of infinite symmetrical groups and condensation,? Comment. Math. Univ. Carol.,22, No. 2, 311?316 (1981). · Zbl 0484.22002
[50] Kh. Drashkovicheva, T. Katrinyak, and M. Kolibiar, ?Boolean algebras and related lattices,? Usporiad. Mnoziny a Zvazy, Bratislava (1985), pp. 7?77.
[51] S. S. Dumitrashku, ?On uniform embeddings of topological algebras,? Studies in Modern Algebra and Geometry. Mathematical Sciences [in Russian], Kishinev (1983), pp. 15?25.
[52] S. S. Dumitrashku and M. M. Choban, ?On free topological algebras with continuous signature,? Mat. Issled., Kishenev, No. 65, 27?53 (1982). · Zbl 0503.08009
[53] L. G. Zambakhidze, ?On relations between dimensions and cardinal-valued functions of spaces embedded in spaces of special type,? Soobshch. AN GruzSSR,100, No. 3, 557?560 (1980). · Zbl 0484.54007
[54] L. G. Zambakhidze, ?On relations between dimensions of free bases of free topological groups,? Soobshch. AN GruzSSR,97, No. 3, 569?572 (1980). · Zbl 0452.54031
[55] L. N. Ivanovskii, ?On a conjecture of P. S. Aleksandrov,? Dokl. AN SSSR,123, No. 5, 785?786 (1958).
[56] G. I. Kats, ?Isomorphic mapping of topological groups into direct products of groups satisfying the first countability axiom,? Usp. Mat. Nauk,8, No. 6, 107?113 (1953).
[57] A. N. Kolmogorov, ?On the linear dimension of topological vector spaces,? Dokl. AN SSSR,120, No. 2, 239?241 (1958).
[58] V. I. Kuz’minov, ?On a conjecture of P. S. Aleksandrov in topological group theory,? Dokl. AN SSSR,125, No. 4, 727?729 (1959).
[59] A. G. Kurosh, Group Theory [in Russian], Nauka, Moscow (1967).
[60] A. G. Leiderman, ?On properties of continuous function spaces,? in: Cardinal Invariants and Mappings of Topological Spaces [in Russian], Izhevsk (1984), pp. 50?54.
[61] A. G. Leiderman, ?On everywhere dense metrizable subspaces of Corson compacta,? Mat. Zametki,38, No. 3, 440?449 (1985).
[62] A. G. Leiderman, ?On properties of Corson compacta,? 5th Tiraspol’ Symp. on General Topology and Its Applications [in Russian], Kishenev (1985), pp. 136?137.
[63] V. I. Malykhin, ?Extremally disconnected and related groups,? Dokl. AN SSSR,220, No. 1, 27?30 (1975).
[64] V. I. Malykhin and V. I. Ponomarev, ?General topology (set-theoretical direction),? J. Sov. Math.,1, No. 4 (1977).
[65] A. I. Mal’tsev, ?Free topological algebras,? Izv. AN SSSR, Ser. Mat.,21, No. 2, 171?198 (1957).
[66] A. A. Markov, ?On free topological groups,? Dokl. AN SSSR,31, No. 4, 299?301 (1941).
[67] A. A. Markov, ?On free topological groups,? Izv. AN SSSR, Ser. Mat.,9, No. 1, 3?64 (1945).
[68] A. A. Milyutin, ?Isomorphism of continuous function spaces over compacta of continuum cardinality,? in: Theory of Functions, Functional Analysis, and Applications [in Russian], No. 2, Kharkov (1966), pp. 150?156.
[69] L. B. Nakhmanson, ?On continuous images of ?-products,? in: Topology and Set Theory [in Russian], Izhevsk (1982), pp. 11?15.
[70] L. B. Nakhmanson, ?Suslin number and calibers of continuous function ring,? Izv. Vuzov, Mat., No. 3, 49?55 (1984).
[71] L. B. Nakhmanson, ?Lindelöf property in function space,? 5th Tiraspol’ Symp. on General Topology and Its Applications [in Russian], Kishinev (1985), p. 183.
[72] L. B. Nakhmanson and N. N. Yakovlev, ?On bicompacta lying in ?-products,? Comment. Math. Univ. Carol.,22, No. 4, 705?719 (1981). · Zbl 0499.54006
[73] O. G. Okunev, ?Hewitt extensions and function spaces,? in: Cardinal Invariants and Mappings of Topological Spaces [in Russian], Izhevsk (1984), pp. 77?78.
[74] O. G. Okunev, ?A method of construction of M-equivalent spaces,? 5th Tiraspol’ Symp. on General Topology and Its Applications [in Russian], Kishenev (1985), p. 189.
[75] O. G. Okunev, On One Method of Construction of Examples of M-Equivalent Spaces [in Russian], Moscow State Univ. (1984). Unpublished manuscript available from VINITI, 8.01.1985, No. 241-85 Dep.
[76] O. G. Okunev, ?On function spaces in the topology of pointwise convergence: Hewitt extension and ?-continuous functions,? Vestn. Mosk. Gos. Univ., Mat., Mekh., No. 4, 78?80 (1985). · Zbl 0582.54010
[77] O. G. Okunev, ?l-equivalence of function spaces,? in: Continuous Functions on Topological Spaces [in Russian], Riga (1986), pp. 123?125.
[78] D. S. Pavlovskii, ?Spaces of open sets and continuous function spaces,? Dokl. AN SSSR,246, No. 4, 815?818 (1979).
[79] D. S. Pavlovskii, ?On continuous function spaces,? Dokl. AN SSSR,253, No. 1, 38?41 (1980).
[80] D. S. Pavlovskii, ?On spaces having linearly homeomorphic continuous function spaces in the topology of pointwise convergence,? Usp. Mat. Nauk,37, No. 2, 185?186 (1982).
[81] B. A. Pasynkov, ?Almost metrizable topological groups,? Dokl. AN SSSR,161, No. 2, 291?294 (1965).
[82] B. A. Pasynkov, ?On spaces with a bicompact transformation group,? Dokl. AN SSSR,231, No. 1, 39?42 (1976).
[83] V. V. Pashenkov, ?On dualities,? Dokl. AN SSSR,222, No. 6, 1295?1298 (1975).
[84] V. V. Pashenkov, ?On the structure of continuous functions on completely regular spaces,? Mat. Zametki,19, No. 6, 863?869 (1976).
[85] A. Pelczynski, Linear Extensions, Linear Averagings and Their Application to Linear Topological Classification of Continuous Function Spaces [Russian translation], Mir, Moscow (1970).
[86] V. G. Pestov, On Structure and Embeddings of Topological Groups [in Russian], Tomskii Univ., Tomsk (1981). Unpublished manuscript available from VINITI, 3.04.1981, No. 1495-81 Dep.
[87] V. G. Pestov, ?Some properties of free topological groups,? Vestn. Mosk. Gos. Univ., Mat., Mekh., No. 1, 35?37 (1982). · Zbl 0499.22001
[88] V. G. Pestov, ?Equality of dim dimensions ofl-equivalent topological spaces,? Dokl. AN SSSR,266, No. 3, 553?556 (1982).
[89] V. G. Pestov, ?Relations between classes of almost metrizable, protectively metrizable, and ?0-representable topological groups,? in: Topol. Spaces and Their Mappings [in Russian], Riga (1983), pp. 80?86. · Zbl 0571.22001
[90] V. G. Pestov, ?Some topological properties preserved by M-equivalence relation,? Usp. Mat. Nauk,39, No. 6, 203?204 (1984). · Zbl 0587.54017
[91] V. G. Pestov, ?Neighborhoods of unity in free groups,? Vestn. Mosk. Gos. Univ., Mat., Mekh., No. 3, 8?10 (1985). · Zbl 0592.22002
[92] V. G. Pestov, ??0-representability and completion of topological groups,? 5th Tiraspol’ Symp. on General Topology and Its Applications [in Russian], Kishenev (1985), pp. 205?207.
[93] V. G. Pestov, ?On the theorem of M. M. Choban on extension of pseudometrics to free universal algebras,? in: Continuous Functions on Topological spaces [in Russian], Riga (1986), pp. 142?146.
[94] V. G. Pestov, ?Free Banach spaces and representations of topological groups,? Funkts. Anal. Prilozhen.,20, No. 1, 81?82 (1986). · Zbl 0635.22005
[95] V. G. Pestov, ?Free topological abelian groups and Pontryagin duality,? Vestn. Mosk. Gos. Univ., Mat., Mekh., No. 1, 3?5 (1986). · Zbl 0599.22003
[96] V. G. Pestov and D. B. Shakhmatov, ?Continuous homomorphic images of a group with a countable base do not exhaust all the groups with countable network,? Vestn. Mosk. Gos. Univ., Mat., Mekh., No. 3, 90?101 (1986). · Zbl 0598.22004
[97] L. S. Pontryagin, Continuous Groups [in Russian], 3rd revised edition, Nauka, Moscow (1973).
[98] E. G. Pytkeev, ?On sequential property of continuous function spaces,? Usp. Mat. Nauk,37, No. 5, 197?198 (1982). · Zbl 0509.54010
[99] E. G. Pytkeev, ?On tightness of continuous function spaces,? Usp. Mat. Nauk,37, No. 1, 157?158 (1982). · Zbl 0501.54008
[100] E. G. Pytkeev, ?Baire property of continuous function spaces,? Mat. Zametki,38, No. 5, 726?740 (1985). · Zbl 0601.54032
[101] D. A. Raikov, ?On completion of topological groups,? Izv. AN SSSR, Ser. Mat.,10, No. 6, 513?518 (1946). · Zbl 0061.04206
[102] D. A. Raikov, ?Free locally convex spaces of uniform spaces,? Mat. Sb.,63, No. 4, 582?590 (1964).
[103] D. A. Raikov, ?A completeness criterion of topological linear spaces and topological abelian groups,? Mat. Zametki,16, No. 1, 101?106 (1974). · Zbl 0305.46009
[104] O. V. Sipacheva, ?Topology on free groups,? 5th Tiraspol’ Symp. on General Topology and Its Applications [in Russian], Kishenev (1985), pp. 278.
[105] O. V. Sipacheva, ?Description of the topology of free topological groups without using universal uniform structures,? in: General Topology. Mappings of Topological Spaces [in Russian], Moscow State Univ. (1986), pp. 122?129.
[106] G. A. Sokolov, ?On Lindelöf spaces of continuous functions,? Mat. Zametki,39, No. 6, 887?894 (1986). · Zbl 0607.54012
[107] M. G. Tkachenko, ?On zero-dimensional topological groups,? Proc. Leningrad Intern. Topological Conf., 23?28 Aug. 1982 [in Russian], Leningrad (1983), pp. 113?118.
[108] M. G. Tkachenko, ?On completeness of free abelian topological groups,? Dokl. AN SSSR,269, No. 2, 299?303 (1983). · Zbl 0521.22002
[109] M. G. Tkachenko, ?On Suslin property in free topological groups over bicompacta,? Mat. Zametki,34, No. 4, 601?607 (1983). · Zbl 0535.22002
[110] M. G. Tkachenko, ?On completeness of topological groups,? Sib. Mat. Zh.,25, No. 1, 146?158 (1984). · Zbl 0566.22005 · doi:10.1007/BF00969517
[111] M. G. Tkachenko, ?On spectral expansion of free topological groups,? Usp. Mat. Nauk,39, No. 2, 191?192 (1984).
[112] M. G. Tkachenko, ?On the topology of free groups over bicompacta,? in: Mappings and Functors [in Russian], Moscow State Univ. (1984), pp. 122?137.
[113] M. G. Tkachenko, ?On some properties of free topological groups,? Mat. Zametki,37, No. 1, 110?118 (1984). · Zbl 0546.22002
[114] M. G. Tkachenko, ?On zero-dimensional free topological groups,? Dokl. Bolg. AN,38, No. 2, 173?174 (1985).
[115] V. V. Tkachuk, ?On one method of constructing examples of M-equivalent spaces,? Usp. Mat. Nauk,38, No. 6, 127?128 (1983). · Zbl 0573.22003
[116] V. V. Tkachuk, ?On cardinal invariants of the type of Suslin number,? Dokl. AN SSSR,270, No. 4, 795?798 (1983). · Zbl 0539.54001
[117] V. V. Tkachuk, ?On multiplicativeness of some properties of spaces of mappings in the topology of pointwise convergence,? Vestn. Mosk. Gos. Univ., Mat., Mekh., No. 6, 36?39 (1984).
[118] V. V. Tkachuk, ?Characterization of Baire properties in Cp(X) by properties of the space X,? in: Cardinal Invariants and Mappings of Topological Spaces [in Russian], Izhevsk (1984), pp. 76?77.
[119] V. V. Tkachuk, ?Duality relative to the functor Cp and cardinal invariants of the type of Suslin number,? Mat. Zametki,37, No. 3, 441?451 (1985). · Zbl 0568.54005
[120] V. V. Tkachuk, ?The least subring of the ring Cp[Cp(X)] containing X?{1} is every-where dense in Cp[Cp(X)],? Vestn. Mosk. Gos. Univ., Mat., Mekh., No. 1, 20?22 (1987).
[121] V. V. Tkachuk and D. B. Shakhmatov, ?When is the space Cp(X) ?-countably compact?? Vestn. Mosk. Gos. Univ., Mat., Mekh., No. 1, 70?72 (1986). · Zbl 0619.54009
[122] V. V. Uspenskii, ?On embeddings in function spaces,? Dokl. AN SSSR,242, No. 3, 545?546 (1978).
[123] V. V. Uspenskii, ?On the frequency spectrum of function spaces,? Vestn. Mosk. Gos. Univ., Mat., Mekh., No. 1, 31?35 (1982).
[124] V. V. Uspenskii, ?The topological group generated by Lindelöf ?-space has the Suslin property,? Dokl. AN SSSR,265, No. 4, 823?826 (1982).
[125] V. V. Uspenskii, ?Characterization of compactness in terms of uniform structure in function space,? Usp. Mat. Nauk,37, No. 4, 183?184 (1982).
[126] V. V. Uspenskii, ?On normality of continuous function spaces,? All-Union School on Function Theory in Honor of 100th Anniversary of Acad. N. N. Luzin [in Russian], 10?19 Sept. 1983, Kemerovo (1983), p. 117.
[127] V. V. Uspenskii, ?On the topology of free locally convex space,? Dokl. AN SSSR,270, No. 6, 1334?1337 (1983).
[128] V. V. Uspenskii, ?On continuous images of Lindelöf topological groups,? Dokl. AN SSSR,285, No. 4, 824?827 (1985).
[129] V. V. Uspenskii, ?On subgroups of free topological groups,? Dokl. AN SSSR,285, No. 5, 1070?1072 (1985).
[130] V. V. Uspenskii, ?Universal topological group with countable base,? Funkts. Anal. Prilozhen.,20, No. 2, 86?87 (1986).
[131] G. M. Khenkin, ?Proof of nonisomorphism of the space of smooth functions on the interval and the square,? Dokl. AN SSSR,172, No. 1, 48?51 (1967).
[132] T. E. Khmyleva, ?Classification of continuous function spaces on ordinal intervals,? Sib. Mat. Zh.,20, No. 3, 624?631 (1979).
[133] V. S. Charin, ?Topological groups,? Itogi Nauki, VINITI,1964, Algebra (1966), pp. 123?160.
[134] M. M. Choban, ?On completion of topological groups,? Vestn. Mosk. Gos. Univ., Mat., Mekh., No. 1, 33?38 (1970). · Zbl 0205.04203
[135] M. M. Choban, ?Topological structure of subsets of topological groups and their factor-spaces,? Dokl. AN SSSR,228, No. 1, 52?55 (1976). · Zbl 0346.22007
[136] M. M. Choban, ?Topological structure of subsets of topological groups and their factor-spaces,? Mat. Issled., Kishenev, No. 44, 117?163 (1977).
[137] M. M. Choban, ?On some questions of topological group theory,? in: General Algebra and Discrete Geometry. Math. Sciences [in Russian], Kishenev (1980), pp. 120?135.
[138] M. M. Choban, ?On the theory of topological algebraic systems,? Tr. Moskovsk. Mat. Obshch.,48, 106?149 (1985).
[139] N. I. Shakenko, ?On topologies on continuous function rings,? 4th Tiraspol’ Symp. on General Topology and Its Applications [in Russian], Kishenev (1979), pp. 162?163.
[140] N. I. Shakenko, ?On topological rings of continuous real functions,? Usp. Mat. Nauk,37, No. 5, 207?208 (1982). · Zbl 0534.54009
[141] B. E. Shapirovskii, ?Special types of embeddings in Tikhonov cubes. Subspaces of ?-products and cardinal invariants,? Topology, Colloq. Math. Soc. J. Bolyai,23, 1055?1086 (1980).
[142] D. B. Shakhmatov, ?Character and pseudocharacter in minimal topological groups,? Mat. Zametki,38, No. 6, 908?914 (1985). · Zbl 0594.22001
[143] D. B. Shakhmatov, ?Precalibers of ?-compact topological groups,? Mat. Zametki,39, No. 6, 859?868 (1986) · Zbl 0605.22003
[144] E. V. Shchepin, ?On ?-metrizable spaces,? Izv. AN SSSR, Ser. Mat.,43, No. 2, 442?478 (1979). · Zbl 0409.54040
[145] R. Engelking, General Topology [Russian translation], Mir, Moscow (1986).
[146] N. N. Yakovlev, ?Properties of subspaces of ?-products determined by means of coverings,? Comment. Math. Univ. Carol.,25, No. 1, 29?53 (1984). · Zbl 0561.54008
[147] N. N. Yakovlev, ?On a game of Telgarsky,? 5th Tiraspol’ Symp. on General Topology and Its Applications [in Russian], Kishenev (1985), p. 278.
[148] A. Alexiewicz and W. Orlicz, ?Sur la continuite et la classification de Baire de fonctions abstraites,? Fund. Math.,35, 105?126 (1948). · Zbl 0031.21903
[149] K. Alster, ?Almost disjoint families and some characterisations of alephs,? Bull. Acad. Pol. Sci., Ser. Math., Astron. Phys.,25, No. 12, 1203?1206 (1977).
[150] K. Alster, ?Some remarks on Eberlein compacts,? Fund. Math.,104, No. 1, 43?46 (1979). · Zbl 0339.54022
[151] K. Alster and R. Pol, ?On function spaces of compact subspaces of ?-products of the real line,? Fund. Math.,107, No. 2, 135?143 (1980). · Zbl 0432.54013
[152] D. Amir and J. Lindenstrauss, ?The structure of weakly compact sets in Banach spaces,? Ann. Math.,88, No. 1, 35?46 (1968). · Zbl 0164.14903 · doi:10.2307/1970554
[153] R. Arens and J. Dugundji, ?Topologies for function spaces,? Pac. J. Math.,1, No. 1, 5?31 (1951). · Zbl 0044.11801 · doi:10.2140/pjm.1951.1.5
[154] S. Argyros, S. Mercourakis, and S. Negrepontis, ?Analytic properties of Corson-compact spaces,? Gen. Topol. Relat. Mod. Anal. and Algebra,5, Berlin (1983), pp. 12?23. · Zbl 0505.46010
[155] S. Argyros and S. Negrepontis, ?On weakly K-countably determined spaces of continuous functions,? Proc. AMS,87, No. 4, 731?736 (1983). · Zbl 0509.54020
[156] A. V. Arhangel’skii, ?On relationship between topological properties of X and Cp(X),? Gen. Topol. Relat. Mod. Anal. Algebra,5, Berlin (1983), pp. 24?36.
[157] A. V. Arhangel’skii, ?Functional tightness, Q-spaces and ?-einbeddings,? Comment. Math. Univ. Carol.,24, No. 1, 105?120 (1983).
[158] A. V. Arhangel’skii and S. P. Franklin, ?Ordinal invariants for topological spaces,? Mich. Math. J.,15, No. 3, 313?320 (1968). · Zbl 0167.51102 · doi:10.1307/mmj/1029000034
[159] A. V. Arhangel’skii and V. V. Tkacuk, ?Calibers and point-finite cellularity of the space Cp(X) and some questions of S. Gul’ko and M. Husek,? Topol. Appl.,23, No. 1, 65?74 (1986). · Zbl 0591.54023 · doi:10.1016/0166-8641(86)90017-9
[160] A. V. Arhangel’skii and V. V. Uspenskii, ?On the cardinality of the Lindelöf subspaces of function spaces,? Comment. Math. Univ. Carol.,27, No. 4, 673?676 (1986).
[161] Y. Benyamini, M. E. Rudin, and M. Wage, ?Continuous images of weakly compact subsets of Banach spaces,? Pac. J. Math.,70, No. 2, 309?324 (1977). · Zbl 0374.46011 · doi:10.2140/pjm.1977.70.309
[162] Y. Benyamini and T. Starbird, ?Embedding weakly compact sets into Hilbert space,? Isr. J. Math.,23, No. 2, 137?141 (1976). · Zbl 0325.46023 · doi:10.1007/BF02756793
[163] J. L. Blasko, ?On ?-spaces and kR-spaces,? Proc. AMS,67, No. 1, 179?186 (1977).
[164] C. J. R. Borges, ?On stratifiable spaces,? Pac. J. Math.,17, No. 1, 1?16 (1966). · Zbl 0175.19802 · doi:10.2140/pjm.1966.17.1
[165] C. J. R. Borges, ?Free topological groups,? J. Austral. Math. Soc.,23, No. 3, 360?365 (1977). · Zbl 0369.22001 · doi:10.1017/S1446788700018991
[166] C. J. R. Borges, ?Free groups, symmetric and reduced products,? J. Austral. Math. Soc.,A28, No. 2, 174?178 (1979). · Zbl 0435.22008 · doi:10.1017/S1446788700015652
[167] J. Bourgain, ?Compact sets of the first Baire class,? Bull. Soc. Math. Belg.,29, No. 2, 135?1443 (1977). · Zbl 0416.54009
[168] J. Bourgain, ?Some remarks on compact sets of the first Baire class,? Bull. Soc. Math. Belg.,30, No. 1, 3?10 (1978). · Zbl 0414.54011
[169] J. Bourgain, D. H. Fremlin, and M. Talagrand, ?Pointwise compact sets of Baire-measurable functions,? Am. J. Math.,100, No. 4, 845?886 (1978). · Zbl 0413.54016 · doi:10.2307/2373913
[170] L. G. Brown, ?Topologically complete groups,? Proc. AMS,35, No. 2, 593?600 (1972). · Zbl 0251.22001 · doi:10.1090/S0002-9939-1972-0308321-0
[171] R. Brown, ?Function spaces and product topologies,? Quart. J. Math.,15, No. 59, 238?250 (1964). · Zbl 0126.38503 · doi:10.1093/qmath/15.1.238
[172] R. Brown, ?Some nonprojective subgroups of free topological groups,? Proc. AMS,52, 433?440 (1975). · Zbl 0278.22001 · doi:10.1090/S0002-9939-1975-0393326-7
[173] H. Buchwalter, ?Parties bornees d’un espace topologique completement regulier,? Semin. Choquet, Fac. Sci., Paris,9, No. 2, 14/01?14/15 (1969?70).
[174] H. Buchwalter, ?Sur le theoreme de Nachbin-Shirota,? C. R. Acad. Sci.,273, No. 3, A145-A147 (1971).
[175] J. Buchwalter and J. Schmets, ?Sur quelques proprietes de l’espace Cs(T),? J. Math. Pure Appl.,52, No. 3, 337?352 (1973). · Zbl 0268.46025
[176] R. C. Buck, ?Bounded continuous functions on a locally compact space,? Mich. Math. J.,5, No. 2, 95?104 (1958). · Zbl 0087.31502 · doi:10.1307/mmj/1028998054
[177] J. Calbrix and J.-P. Troallic, ?Applications separement continues,? C. R. Acad. Sci.,AB288, No. 13, A647-A648 (1979). · Zbl 0421.54009
[178] J. P. R. Christensen, Topology and Borel Structure, North-Holland, Amsterdam (1974).
[179] J. P. R. Christensen, ?Joint continuity of separately continuous functions,? Proc. AMS,82, No. 3, 455?4612 (1981). · Zbl 0472.54007 · doi:10.1090/S0002-9939-1981-0612739-1
[180] J. P. R. Christensen, ?Theorems of Namioka and R. E. Johnson type for upper semicontinuous and compact valued set-valued mappings,? Proc. AMS,86, No. 4, 649?655 (1982). · Zbl 0506.54016 · doi:10.1090/S0002-9939-1982-0674099-0
[181] J. P. R. Christensen and P. S. Kenderov, ?Dense strong continuity of mappings and the Radon-Nikodym property,? Math. Scand.,54, No. 1, 70?78 (1984). · Zbl 0557.46016 · doi:10.7146/math.scand.a-12041
[182] K. Ciesielski and R. Pol, ?A weakly Lindelöf function space C(K) without any continuous injection into C0(?),? Bull. Acad. Pol. Sci., Ser. Math., Astron. Phys.,32, No. 11?12, 681?688 (1984). · Zbl 0571.54014
[183] M. M. Coban and P. S. Kenderov, ?Generic Gateaux differentiability of convex functionals in C(T) and the topological properties of T,? Mat. i Mat. Obraz., Proc. 15th Conf. Math. Union Bulgaria, Sl”nchev Bryag, 6?9 April 1986, Sofia (1986). · Zbl 0638.46032
[184] H. H. Corson, ?The weak topology of a Banach space,? Trans. AMS,10, No. 1, 1?15 (1961). · Zbl 0104.08502 · doi:10.1090/S0002-9947-1961-0132375-5
[185] H. H. Corson, ?Normality in subsets of product spaces,? Am. J. Math.,81, No. 3, 785?796 (1959). · Zbl 0095.37302 · doi:10.2307/2372929
[186] H. H. Corson and J. Lindenstrauss, ?On simultaneous extension of continuous functions,? Bull. AMS,71, No. 3, 542?545 (1965). · Zbl 0132.09301 · doi:10.1090/S0002-9904-1965-11321-0
[187] H. H. Corson and J. Lindenstrauss, ?On function spaces which are Lindelöf spaces,? Trans. AMS,121, No. 2, 476?491 (1966). · Zbl 0144.37102
[188] H. H. Corson and J. Lindenstrauss, ?Continuous selections with nonmetrisable range,? Trans. AMS,121, No. 2, 492?504 (1966). · Zbl 0148.16803 · doi:10.1090/S0002-9947-1966-0187214-8
[189] H. H. Corson and J. Lindenstrauss, ?On weakly compact subsets of Banach spaces,? Proc. AMS,17, No. 2, 407?423 (1966). · Zbl 0186.44703 · doi:10.1090/S0002-9939-1966-0199669-9
[190] G. Debs, ?Espaces K-analitiques et espaces de Baire de fonctions continues,? Mathematika,32, 218?228 (1985). · Zbl 0603.46033 · doi:10.1112/S0025579300011013
[191] G. Debs, ?Pointwise and uniform convergence on a Corson compact space,? Topol. Appl.,23, No. 3, 299?303 (1986). · Zbl 0613.54007 · doi:10.1016/0166-8641(85)90047-1
[192] G. Debs, ?Points de continuite d’une fonction separement continue,? Proc. AMS,97, No. 1, 167?176 (1986). · Zbl 0592.54012
[193] J. Diestel, Geometry of Banach Spaces ? Selected Topics, Lect. Notes Math., 485 (1975). · Zbl 0307.46009
[194] J. Dijkstra, T. Grilliot, D. Lutzer, and J. van Mill, ?Function spaces of low Borel complexity,? Proc. AMS,94, No. 4, 703?710 (1985). · Zbl 0525.54010 · doi:10.1090/S0002-9939-1985-0792287-2
[195] A. Dold and R. Thom, ?Quasifaserungen und unendliche symmetrische Produkte,? Ann. Math.,67, No. 2, 239?281 (1958). · Zbl 0091.37102 · doi:10.2307/1970005
[196] R. M. Dudley, ?Continuity of homomorphisms,? Duke Math. J.,28, No. 4, 587?594 (1961). · Zbl 0103.01702 · doi:10.1215/S0012-7094-61-02859-9
[197] W. F. Eberlein, ?Weak compactness in Banach Spaces. I,? Proc. Nat. Acad. Sci. (USA),33, 51?53 (1947). · Zbl 0029.26902 · doi:10.1073/pnas.33.3.51
[198] E. E. Enochs, ?Homotopy groups of compact Abelian groups,? Proc. AMS,15, No. 6, 878?881 (1964). · doi:10.1090/S0002-9939-1964-0169240-1
[199] T. Fay, E. T. Ordman, and B. V. Smith Thomas, ?The free topological groups over rationals,? Gen. Topol. Appl.,10, No. 1, 33?47 (1979). · Zbl 0403.22003 · doi:10.1016/0016-660X(79)90027-8
[200] K. Floret, Weakly Compact Sets, Lect, Notes Math.,801 (1980).
[201] D. H. Fremlin, ?Pointwise compact sets of measurable functions,? Manusc. Math.,15, No. 3, 219?242 (1975). · Zbl 0303.28006 · doi:10.1007/BF01168675
[202] Z. Frolik, ?Stone-Weierstrass theorems for C(X) with the sequential topology,? Proc. AMS,27, No. 3, 486?494 (1971). · Zbl 0211.54501 · doi:10.2307/2036480
[203] F. Galvin and A. W. Miller, ??-sets and other singular sets of real numbers,? Topol. Appl.,17, 145?155 (1984). · Zbl 0551.54001 · doi:10.1016/0166-8641(84)90038-5
[204] B. R. Gelbaum, ?Free topological groups,? Proc. AMS,12, No. 5, 737?743 (1961). · Zbl 0106.02604 · doi:10.1090/S0002-9939-1961-0140607-8
[205] J. Gerlits, ?Some properties of C(X). II,? Topol. Appl.,15, No. 3, 255?262 (1983). · Zbl 0505.54017 · doi:10.1016/0166-8641(83)90056-1
[206] J. Gerlits and Zs. Nagy, ?Some properties of C(X), I,? Topol. Appl.,14, No. 2, 151?161 (1982). · Zbl 0503.54020 · doi:10.1016/0166-8641(82)90065-7
[207] L. Gillman and M. Jerison, Rings of Continuous Functions, Van Nostrand, NY (1960). · Zbl 0093.30001
[208] G. Godefroy, ?Compacts de Rosenthal,? Pac. J. Math.,91, No. 2, 293?206 (1980). · Zbl 0475.46003 · doi:10.2140/pjm.1980.91.293
[209] G. Godefroy and M. Talagrand, ?Espaces de Banach representables,? Isr. J. Math.,41, No. 4, 321?330 (1982). · Zbl 0498.46016 · doi:10.1007/BF02760538
[210] A. Grothendieck, ?Criteres de compacticite dans les espace fonctionnels generaux,? Am. J. Math.,74, 168?186 (1952). · Zbl 0046.11702 · doi:10.2307/2372076
[211] A. Grothendieck, ?Sur les applications lineaires faiblement compactes d’espaces du type C(K),? Can. J. Math.,5, No. 2, 129?173 (1953). · Zbl 0050.10902 · doi:10.4153/CJM-1953-017-4
[212] A. Grothendieck, Espaces Vectoriels Topologiques, Inst. Mat. Pura e Apl. Univ. Sao Paulo (1954). · Zbl 0058.33401
[213] G. Gruenhage, ?Covering properties on X2?, W-sets, and compact subsets of ?-products,? Topol. and Appl.,17, No. 3, 287?304 (1984). · Zbl 0547.54016 · doi:10.1016/0166-8641(84)90049-X
[214] G. Gruenhage, ?Games, covering properties and Eberlein compacts,? Topol. and Appl.,23, No. 3, 291?298 (1986). · Zbl 0604.54022 · doi:10.1016/0166-8641(85)90046-X
[215] D. Gulick, ?The ?-compact topology and its relatives,? Math. Scand.,30, No. 2, 159?176 (1972). · Zbl 0253.46045 · doi:10.7146/math.scand.a-11072
[216] J. A. Guthrie, ?Ascoli theorems and the pseudocharacter of mapping spaces,? Bull. Austral. Math. Soc.,10, No. 3, 403?408 (1974). · Zbl 0284.54008 · doi:10.1017/S0004972700041083
[217] J. A. Guthrie, ?Mapping spaces and CS-networks,? Pac. J. Math.,47, No. 2, 465?471 (1973). · Zbl 0253.54025 · doi:10.2140/pjm.1973.47.465
[218] A. W. Hager, ?Approximation of real continuous functions on Lindelöf spaces,? Proc. AMS,22, No. 1, 156?163 (1969). · Zbl 0175.42103
[219] J. Hagler, ?On the structure of S and C(S) for S dyadic,? Trans. AMS,214, 415?428 (1975).
[220] J. Hagler and F. Sullivan, ?Smoothness and weak sequential compactness,? Proc. AMS,78, No. 4, 497?503 (1980). · Zbl 0463.46010
[221] C. E. Hall, ?Protective topological groups,? Proc. AMS,18, No. 3, 425?431 (1967). · doi:10.1090/S0002-9939-1967-0212119-X
[222] M. Hall, ?A topology for free groups and related groups,? Ann. Math.,52, No. 1, 127?139 (1951). · doi:10.2307/1969513
[223] Z. Hao-Zuan, ?On the small diagonals,? Topol. Appl.,13, No. 3, 283?293 (1982). · Zbl 0495.54028 · doi:10.1016/0166-8641(82)90036-0
[224] J. P. L. Hardy, ?The free topological group on a cell complex,? Bull. Austral. Math. Soc.,11, No. 3, 455?463 (1974). · Zbl 0283.54015 · doi:10.1017/S0004972700044087
[225] J. P. L. Hardy and S. A. Morris, ?The free topological group on a simply connected space,? Proc. AMS,55, No. 1, 155?159 (1976). · Zbl 0322.57028 · doi:10.1090/S0002-9939-1976-0424993-8
[226] J. P. L. Hardy, S. A. Morris, and H. B. Thompson, ?Applications of the Stone-?ech compactification to free topological groups,? Proc. AMS,55, No. 1, 160?164 (1976). · Zbl 0333.22001
[227] S. Hartman and J. Mycielsky, ?On the imbedding of topological groups into connected topological groups,? Colloq. Math.,5, No. 2, 167?169 (1958).
[228] R. Haydon, ?Compactness in Cs(T) and applications,? Rubls Dep. Math.,9, No. 1, 105?113 (1972).
[229] R. Haydon, ?Trois exemples dans la theorie des espaces de fonctions continues,? C. R. Acad. Sci.,276, No. 9, A685-A687 (1973). · Zbl 0246.46011
[230] R. Haydon, ?On dual L1-spaces and injective bidual Banach spaces,? Isr. J. Math.,31, No. 2, 142?152 (1978). · Zbl 0407.46018 · doi:10.1007/BF02760545
[231] H. Herrlich, ?Topological functors,? Gen. Topol. Appl.,4, No. 2, 125?142 (1974). · Zbl 0288.54003 · doi:10.1016/0016-660X(74)90016-6
[232] H. Herrlich, R. Nakagawa, G. E. Stecker, and T. Titcomb, ?Equivalence of topologically algebraic and semi-topological functors,? Can. J. Math.,32, No. 1, 34?39 (1980). · Zbl 0435.18002 · doi:10.4153/CJM-1980-004-x
[233] E. Hewitt, ?Rings of real-valued continuous functors, I,? Trans. AMS,64, No. 1, 45?99 (1948). · Zbl 0032.28603 · doi:10.1090/S0002-9947-1948-0026239-9
[234] K. H. Hofmann, ?An essay on free compact groups,? Lect. Notes Math.,915, 171?197 (1982). · Zbl 0498.22004 · doi:10.1007/BFb0092879
[235] K. H. Hofmann and S. A. Morris, ?Free compact groups, I: Free compact Abelian groups,? Topol. Appl.,23, No. 1, 41?64 (1986). · Zbl 0589.22003 · doi:10.1016/0166-8641(86)90016-7
[236] D. C. Hunt and S. A. Morris, ?Free subgroups of free topological groups,? Lect. Notes Math.,372, 377?387 (1974). · doi:10.1007/978-3-662-21571-5_37
[237] D. C. Hunt, S. A. Morris, A. J. van der Poorten, ?Closed subgroups of products of reals,? Bull. London Math. Soc.,7, No. 2, 124?128 (1975). · Zbl 0305.22003 · doi:10.1112/blms/7.2.124
[238] W. Hurewicz, ?Uber Folgen stetiger Funktionen,? Fund. Math.,9, 193?204 (1927). · JFM 53.0562.03
[239] M. Husek, ?Topological spaces without ?-accessible diagonal,? Comment. Math. Univ. Carol.,18, No. 4, 777?788 (1977).
[240] T. A. Ionescu, ?On pointwise convergence, compactness and equicontinuity in the lifting topology, I,? Z. Wahrsheinlichkeitstheor. und verw. Geb.,26, No. 3, 197?205 (1973). · Zbl 0289.46030 · doi:10.1007/BF00532722
[241] A. Irudayanathan, ?Cover-close topologies for function spaces,? Gen. Topol. Appl.,10, No. 3, 275?282 (1979). · Zbl 0409.54022 · doi:10.1016/0016-660X(79)90039-4
[242] A. Irudayanathan and S. A. Naimpally, ?Connected-open topology for function spaces,? Proc. Konikl. Nederl. Acad. Wet.,A69, No. 1, 22?24 (1966). · Zbl 0136.19301
[243] J. R. Isbell, ?Meet-continuous lattices,? Symp. Math., Ist. Naz. Alta Mat.,16 (1975), pp. 41?54.
[244] J. R. Isbell, ?Function spaces and adjoints,? Math. Scand.,36, No. 2, 317?339 (1975). · Zbl 0309.54016 · doi:10.7146/math.scand.a-11581
[245] C. Joiner, ?Free topological groups and dimension,? Trans. AMS,220, 401?418 (1976). · Zbl 0331.54026 · doi:10.1090/S0002-9947-1976-0412322-X
[246] H. J. K. Junilla, J. C. Smith, and R. Telgarsky, ?Closure-preserving covers by small sets,? Topol. Appl.,23, No. 3, 237?262 (1986). · Zbl 0609.54019 · doi:10.1016/0166-8641(85)90042-2
[247] S. Kakutani, ?Free topological groups and infinite direct products of topological groups,? Proc. Imp. Acad., Tokyo,20, 595?598 (1944). · Zbl 0063.03105 · doi:10.3792/pia/1195572799
[248] E. Katz and S. A. Morris, ?Free products of k?-topological groups with normal amalgamation,? Topol. Appl.,15, No. 2, 189?196 (1983). · Zbl 0503.22002 · doi:10.1016/0166-8641(83)90036-6
[249] P. S. Kenderov, ?The set-valued monotone mappings are almost everywhere single-valued,? Dokl. Bolg. AN,27, No. 9, 1173?1175 (1974). · Zbl 0339.47024
[250] P. S. Kenderov, ?Dense strong continuity of pointwise continuous mappings,? Pac. J. Math.,89, No. 1, 111?130 (1980). · Zbl 0458.54011 · doi:10.2140/pjm.1980.89.111
[251] P. S. Kenderov, ?Continuitylike properties of set-valued mappings,? Serdika B”lg. Mat. Spisanie,9, No. 2, 149?160 (1980).
[252] W. F. Lamartin, On the Foundations of k-Group Theory, Rozpr. Mat.,146 (1977). · Zbl 0394.22001
[253] J. D. Lawson, ?T0-spaces and pointwise convergence,? Topol. Appl.,21, No. 1, 73?76 (1985). · Zbl 0575.54013 · doi:10.1016/0166-8641(85)90059-8
[254] J. P. Lee and Z. Piotrowski, ?A note on spaces related to Namioka spaces,? Bull. Austral. Math. Soc.,31, No. 2, 285?292 (1985). · Zbl 0549.54009 · doi:10.1017/S0004972700004755
[255] A. G. Leiderman and G. A. Sokolov, ?Adequate families of sets and Corson compacts,? Comment. Math. Univ. Carol.,25, No. 2, 233?246 (1984). · Zbl 0586.54022
[256] A. Lelek, ?Some cover properties of spaces,? Fund. Math.,64, No. 2, 209?218 (1969). · Zbl 0175.49603
[257] J. Lindenstrauss, ?Weakly compact sets ? their topological properties and the Banach spaces they generate,? Ann. Math. Stud.,69, 235?273 (1972). · Zbl 0232.46019
[258] D. J. Lutzer and R. A. McCoy, ?Category in function spaces,? Pac. J. Math.,89, No. 2, 1?24 (1980). · Zbl 0481.54017 · doi:10.2140/pjm.1980.89.1
[259] D. J. Lutzer, J. van Mill, and R. Pol, ?Descriptive complexity of function spaces,? Trans. AMS,291, 121?128 (1985). · Zbl 0574.54042 · doi:10.1090/S0002-9947-1985-0797049-2
[260] J. Mack, S. Morris, and E. T. Ordman, ?Free topological groups and the protective dimension of locally compact Abelian group,? Proc. AMS,40, No. 1, 303?308 (1973). · Zbl 0263.22001 · doi:10.1090/S0002-9939-1973-0320216-6
[261] W. Marciszewski, ?A pre-Hilbert space without any continuous map onto its own square,? Bull. Acad. Pol. Sci.,31, No. 9?12, 393?397 (1983). · Zbl 0548.46003
[262] W. Marciszewski, ?A function space C(K) not weakly homeomorphic to C(K){\(\times\)}C(K),? Univ. Warszawski, Inst. Math., Preprint 11/86, Warszawa (1986).
[263] D. Marxen, ?Free uniform semigroups and free uniform groups,? Bull. Inst. Math. Acad. Sinica,3, 213?225 (1975). · Zbl 0327.22005
[264] D. Marxen, ?Neighborhoods of the identity of the free Abelian topological groups,? Math. Slovaca (CSSR),26, No. 3, 247?356 (1976). · Zbl 0345.22001
[265] R. D. Mauldin, ?On the Borel subspaces of algebraic structures,? Indiana Univ. Math. J.,29, No. 2, 261?265 (1980). · Zbl 0433.22001 · doi:10.1512/iumj.1980.29.29017
[266] R. A. McCoy, ?K-space function space,? Int. J. Math. Sci.,3, 701?711 (1980). · Zbl 0449.54013 · doi:10.1155/S0161171280000506
[267] R. A. McCoy, ?Complete function spaces,? Int. J. Math. Sci.,6, 271?278 (1983). · Zbl 0531.54015 · doi:10.1155/S0161171283000228
[268] R. A. McCoy and I. Ntantu, ?Completeness of function spaces,? Topol. Appl.,22, No. 2, 191?206 (1986). · Zbl 0621.54011 · doi:10.1016/0166-8641(86)90009-X
[269] P. O’Meara, ?On paracompactness in function spaces with the compact-open topology,? Trans. AMS,29, No. 1, 183?189 (1971).
[270] P. R. Meyer, ?Function spaces and the Alexandroff-Urysohn conjecture,? Annali Mat. Pura Appl.,86, 25?30 (1970). · doi:10.1007/BF02415705
[271] E. Michael, ??0-spaces,? J. Math. Mech.,15, No. 6, 983?1002 (1966).
[272] E. Michael, ?On k-spaces, kR-spaces and k(X),? Pac. J. Math.,47, No. 2, 487?498 (1973). · Zbl 0262.54017 · doi:10.2140/pjm.1973.47.487
[273] E. Michael and M. E. Rudin, ?A note on Eberlein compacts,? Pac. J. Math.,72, No. 2, 487?495 (1977). · Zbl 0345.54020 · doi:10.2140/pjm.1977.72.487
[274] A. N. Milgram, ?Multiplicative semigroups of continuous functions,? Duke Math. J.,16, No. 2, 373?383 (1949). · Zbl 0033.28301 · doi:10.1215/S0012-7094-49-01638-5
[275] J. van Mill, ?A homogeneous Eberlein compact space which is not metrisable,? Pac. J. Math.,101, No. 1, 141?146 (1982). · Zbl 0495.54020 · doi:10.2140/pjm.1982.101.141
[276] J. van Mill, ?Closed images of topological groups,? Proc. Colloq. Topol. and Appl., Eger, Hungary, 1983, Colloq. Math. Soc. J. Bolyai,41, 419?426 (1984).
[277] J. van Mill and R. Pol, ?The Baire category theorem in products of linear spaces and topological groups,? Topol. Appl.,22, No. 3, 267?282 (1986). · Zbl 0589.54040 · doi:10.1016/0166-8641(86)90025-8
[278] P. R. Misra, ?On isomorphism theorems for C(X),? Acta Math. Acad. Sci. Hung.,39, No. 4, 379?380 (1982). · Zbl 0479.54011 · doi:10.1007/BF01896704
[279] S. A. Morris, ?Varieties of topological groups, I,? Bull. Austral. Math. Soc.,1, No. 2, 145?160 (1969). · Zbl 0172.31404 · doi:10.1017/S0004972700041393
[280] S. A. Morris, ?Varieties of topological groups, III,? Bull. Austral. Math. Soc.,2, No. 2, 165?178 (1970). · Zbl 0186.32901 · doi:10.1017/S0004972700041782
[281] S. A. Morris, ?Varieties of topological groups, II,? Bull. Austral. Math. Soc.,2, No. 1, 1?13 (1970). · Zbl 0179.04904 · doi:10.1017/S0004972700041563
[282] S. A. Morris, ?Free compact abelian groups,? Mat. Cas.,22, No. 2, 141?147 (1972).
[283] S. A. Morris, ?Varieties of topological groups and left-adjoint functors,? J. Austral. Math. Soc.,16, No. 2, 220?227 (1973). · Zbl 0274.22003 · doi:10.1017/S1446788700014269
[284] S. A. Morris, ?Remarks on varieties of topological groups,? Mat. Cas.,24, No. 1, 7 (1974).
[285] S. A. Morris, E. T. Ordman, and H. B. Thompson, ?The topology of free products of topological groups,? Lect. Notes Math.,372, 504?515 (1974). · Zbl 0289.22002 · doi:10.1007/978-3-662-21571-5_53
[286] S. A. Morris and H. B. Thompson, ?Invariant metrics on free topological groups,? Bull. Austral. Math. Soc.,9, No. 1, 83?88 (1973). · Zbl 0255.22002 · doi:10.1017/S0004972700042908
[287] S. A. Morris and H. B. Thompson, ?Metrizability of subgroups of free topological groups,? Bull. Austral. Math. Soc.,33, No. 1, 103?112 (1986). · Zbl 0577.22006 · doi:10.1017/S0004972700002926
[288] J. Mycielski, ?Independent sets in topological algebras,? Fund. Math.,55, No. 2, 139?147 (1964). · Zbl 0124.01301
[289] L. Nachbin, ?Topological vector spaces of continuous functions,? Proc. Nat. Acad. Sci (USA),40, No. 6, 471?474 (1954). · Zbl 0055.09803 · doi:10.1073/pnas.40.6.471
[290] J. Nagata, ?On lattices of functions on topological spaces and of functions on uniform spaces,? Osaka Math. J.,1, No. 2, 166?181 (1949). · Zbl 0036.38602
[291] S. A. Naimpally, ?Graph topology for function spaces,? Trans. AMS,123, No. 1, 267?272 (1966). · Zbl 0151.29703 · doi:10.1090/S0002-9947-1966-0192466-4
[292] T. Nakayama, ?Note on free topological groups,? Proc. Imp. Acad. Jpn.,19, 471?475 (1943). · Zbl 0063.05899 · doi:10.3792/pia/1195573368
[293] I. Namioka, ?Neighborhoods of extreme points,? Isr. J. Math.,5, No. 3, 145?152 (1967). · Zbl 0177.40501 · doi:10.1007/BF02771100
[294] I. Namioka, ?Right topological groups, distal flows, and a fixed-point theorem,? Math. Syst. Theory,6, No. 3, 193?209 (1972). · Zbl 0239.22001 · doi:10.1007/BF01706088
[295] I. Namioka, ?Separate continuity and joint continuity,? Pac. J. Math.,51, No. 2, 515?531 (1974). · Zbl 0294.54010 · doi:10.2140/pjm.1974.51.515
[296] S. Negrepontis and A. Tsarpalias, ?A nonlinear version of the Amir-Lindenstrauss method,? Isr. J. Math.,38, No. 1?2, 82?94 (1981). · Zbl 0508.46009 · doi:10.1007/BF02761851
[297] P. Nickolas, ?Subgroups of the free topological group on [0, 1],? J. London Math. Soc.,12, No. 2, 199?205 (1976). · Zbl 0318.22002 · doi:10.1112/jlms/s2-12.2.199
[298] P. Nickolas, ?Reflexivity of topological groups,? Proc. AMS,65, No. 1, 137?141 (1977). · Zbl 0369.22002 · doi:10.1090/S0002-9939-1977-0486276-0
[299] N. Noble, ?k-groups and duality,? Trans. AMS,151, No. 2, 551?561 (1970).
[300] N. Noble, ?The density character of function spaces,? Proc. AMS,42, No. 1, 228?233 (1974). · Zbl 0278.54016 · doi:10.1090/S0002-9939-1974-0328855-4
[301] E. C. Nummela, ?The projective dimension of a compact abelian group,? Proc. AMS,38, No. 3, 452?456 (1973). · Zbl 0255.22007 · doi:10.1090/S0002-9939-1973-0313362-4
[302] E. C. Nummela, ?K-groups generated by K-spaces,? Trans. AMS,201, 279?289 (1975). · Zbl 0292.22003
[303] E. C. Nummela, ?The completion of a topological group,? Bull. Austral. Math. Soc.,21, No. 3, 407?417 (1980). · Zbl 0424.22002 · doi:10.1017/S0004972700006250
[304] E. C. Nummela, ?Uniform free topological groups and Samuel compactification,? Topol. Appl.,13, No. 1, 77?83 (1982). · Zbl 0471.22001 · doi:10.1016/0166-8641(82)90009-8
[305] P. Nyikos, ?Metrizability and the Frechet-Urysohn property in topological groups,? Proc. AMS,83, No. 4, 793?801 (1981). · Zbl 0474.22001
[306] E. T. Ordman, ?Free products of topological groups with equal uniformities, I, II,? Colloq. Math.,31, No. 1, 37?49 (1974). · Zbl 0261.22001
[307] E. T. Ordman, ?Free products of topological groups which are k?-spaces,? Trans. AMS,191, No. 1, 61?73 (1974). · Zbl 0287.22003
[308] E. T. Ordman, ?Free k-groups and free topological groups,? Gen. Topol. and Appl.,5, No. 4, 205?219 (1975). · Zbl 0306.22003 · doi:10.1016/0016-660X(75)90021-5
[309] E. T. Ordman and B. V. Smith-Thomas, ?Sequential conditions and free topological groups,? Proc. AMS,79, No. 2, 319?326 (1980). · doi:10.1090/S0002-9939-1980-0565363-2
[310] J. C. Oxtoby, ?Cartesian products of Baire spaces,? Fund. Math.,49, No. 2, 157?166 (1961).
[311] R. Pol, ?On a question of H. H. Corson and some related matters,? Fund. Math.,109, No. 2, 143?154 (1980).
[312] R. Pol, ?Normality in function spaces,? Fund. Math.,84, No. 2, 145?155 (1974).
[313] R. Pol, ?Concerning function spaces on separable compact spaces,? Bull. Acad. Pol. Sci., Ser. Math., Astron. Phys.,25, No. 10, 993?997 (1977).
[314] R. Pol, ?The Lindelöf property and its convex analogue in function spaces with the weak topology,? Topology, 4th Colloq., Budapest, 1978, Vol. 2, Amsterdam (1980), pp. 965?969.
[315] R. Pol, ?A function space C(X) which is weakly Lindelöf but not weakly compactly generated,? Stud. Math. (PRL),64, No. 3, 279?285 (1979). · Zbl 0424.46011
[316] R. Pol, ?Note on the spaces P(S) of regular probability measures whose topology is determined by countable subsets,? Pac. J. Math.,100, No. 1, 185?201 (1982). · Zbl 0522.46019 · doi:10.2140/pjm.1982.100.185
[317] R. Pol, ?A theorem on the weak topology of C(X) for compact scattered X,? Fund. Math.,106, No. 2, 135?140 (1980).
[318] R. Pol, ?An infinite-dimensional pre-Hilbert space not homeomorphic to its own square,? Proc. AMS,90, No. 3, 450?454 (1984). · Zbl 0528.54032 · doi:10.1090/S0002-9939-1984-0728367-6
[319] R. Pol, ?On pointwise and weak topology in function spaces,? Univ. Warszawski, Inst. Mat., Preprint 4/84, Warszawa (1984).
[320] R. Pol, ?Note on compact sets of first Baire class functions,? Proc. AMS,96, No. 1, 152?154 (1986). · Zbl 0584.54014 · doi:10.1090/S0002-9939-1986-0813828-3
[321] D. Preiss and P. Simon, ?A weakly pseudocompact subspace of Banach space is weakly compact,? Comment. Math. Univ. Carol.,15, No. 4, 603?609 (1974). · Zbl 0306.54033
[322] Iv. Prodanov and L. N. Stojanov, ?Every minimal Abelian group is precompact,? Dokl. Bolg. AN,37, 23?26 (1984).
[323] J. D. Pryce, ?A device of R. J. Whitley’s applied to pointwise compactness in spaces of continuous functions,? Proc. AMS,23, No. 3, 532?546 (1971). · Zbl 0221.46012
[324] V. Ptak, ?On a theorem of W. F. Eberlein,? Stud. Math.,14, No. 2, 276?284 (1954).
[325] V. Ptak, ?A combinatorial lemma on the existence of convex means and its application to weak compactness,? Convexity, AMS, Providence, RI (1963), pp. 437?450.
[326] E. G. Pytkeev, ?On some properties of spaces of continuous functions,? Proc. Leningrad Intern. Topol. Conf., 23?27 Aug. 1982. · Zbl 0501.54008
[327] H. P. Rosenthal, ?The hereditary problem for weakly compactly generated Banach spaces,? Compos. Math.,28, No. 1, 88?111 (1974).
[328] H. P. Rosenthal, ?The Banach space C(K) and LP(?),? Bull. AMS,81, No. 5, 763?781 (1975). · Zbl 0334.46033 · doi:10.1090/S0002-9904-1975-13824-9
[329] H. P. Rosenthal, ?Pointwise compact subsets of the first Baire class,? Am. J. Math.,99, No. 2, 362?378 (1977). · Zbl 0392.54009 · doi:10.2307/2373824
[330] H. P. Rosenthal, ?Some recent discoveries in the isomorphic theory of Banach spaces,? Bull. AMS,84, No. 5, 803?831 (1978). · Zbl 0391.46016 · doi:10.1090/S0002-9904-1978-14521-2
[331] J. Saint Raimond, ?Jeux topologiques et espaces de Namioka,? Proc. AMS,87, No. 3, 499?504 (1983). · Zbl 0511.54007 · doi:10.1090/S0002-9939-1983-0684646-1
[332] P. Samuel, ?On universal mappings and free topological groups,? Bull. AMS,54, No. 6, 591?598 (1948). · Zbl 0031.41702 · doi:10.1090/S0002-9904-1948-09052-8
[333] D. B. Shakhmatov, ?A pseudocompact Tychonoff space all countable subsets of which are closed and C*-embedded,? Topol. Appl.,22, No. 3, 139?144 (1986). · Zbl 0586.54020 · doi:10.1016/0166-8641(86)90004-0
[334] S. Scheinberg, ?Homeomorphism and isomorphism of Abelian groups,? Can. J. Math.,26, No. 6, 1515?1519 (1974). · Zbl 0259.22002 · doi:10.4153/CJM-1974-147-4
[335] T. Shirota, ?On locally convex vector spaces of continuous functions,? Proc. Jpn. Acad.,30, No. 4, 294?298 (1954). · Zbl 0057.33801 · doi:10.3792/pja/1195526112
[336] J. Schmets, Espaces de Fonctions Continues, Lect. Notes Math.,519 (1976). · Zbl 0334.46022
[337] Z. Semadeni, Banach Spaces of Continuous Functions, Vol. 1, Monogr. Math.,55 (1971). · Zbl 0225.46030
[338] W. Sierpinski, ?Sur une suite infinite de fonctions de class 1 dont toute fonction d’accumulation est non measurable,? Fund. Math.,33, 104?105 (1945).
[339] P. Simon, ?On continuous images of Eberlein compacts,? Comment. Math. Univ. Carol.,17, No. 1, 179?194 (1976). · Zbl 0322.54014
[340] G. A. Sokolov, ?On some classes of compact spaces lying in ?-products,? Comment. Math. Univ. Carol.,25, No. 2, 219?231 (1984). · Zbl 0577.54014
[341] L. Stojanov, ?Cardinalities of minimal abelian groups,? Mat. i Mat. Obraz., 10th Conf. of Bulgarian Math. Union, Sl”nchev Bryag, 1981, Sofia (1981), pp. 203?208.
[342] S. Swierczkowski, ?Topologies in free algebras,? Proc. London Math. Soc.,14, No. 55, 566?576 (1964). · Zbl 0123.09902 · doi:10.1112/plms/s3-14.3.566
[343] M. Talagrand, ?Sur une conjecture de H. H. Corson,? Bull. Sci. Math.,99, No. 4, 211?212 (1975).
[344] M. Talagrand, ?Espaces de Banach faiblement K-analitiques,? C. R. Acad. Sci.,284, No. 13, A405-A407 (1977).
[345] M. Talagrand, ?Deux exemples de fonctions convex,? C. R. Acad. Sci.,AB288, No. 8, A239-A251 (1979). · Zbl 0367.54004
[346] M. Talagrand, ?Deux generalizations d’une theoreme de I. Namioka,? Pac. J. Math.,81, 239?251 (1979). · Zbl 0367.54004 · doi:10.2140/pjm.1979.81.239
[347] M. Talagrand, ?Espaces de Banach faiblement K-analitiques,? Ann. Math.,110, No. 3, 407?438 (1979). · Zbl 0393.46019 · doi:10.2307/1971232
[348] M. Talagrand, ?A new countably determined Banach space,? Isr. J. Math.,47, No. 1, 75?80 (1984). · Zbl 0537.46019 · doi:10.1007/BF02760563
[349] M. Talagrand, ?Propriete de Baire et propriete de Namioka,? Ann. Math.,270, 159?174 (1985). · Zbl 0582.54008 · doi:10.1007/BF01456180
[350] B. V. S. Thomas, ?Free topological groups,? Gen. Topol. Appl.,4, No. 1, 51?72 (1974). · Zbl 0276.54044 · doi:10.1016/0016-660X(74)90005-1
[351] H. B. Thompson, ?A remark on free topological group with no small subgroups,? J. Austral. Math. Soc.,18, No. 4, 482?484 (1974). · Zbl 0297.22001 · doi:10.1017/S1446788700029219
[352] M. G. Tkacenko, ?Some results on inverse spectra, II,? Comment. Math. Univ. Carol.,22, No. 4, 819?841 (1981).
[353] M. G. Tkacenko, ?Free topological groups and related topics,? Proc. Colloq. Topol. Appl., Eger, Hungary, 1983, Colloq. Math. Soc. J. Bolyai,41, 609?623 (1984).
[354] M. G. Tkacenko, ?On topologies of free groups,? Czechoslov. Math. J.,34, No. 4, 541?551 (1984).
[355] V. V. Tkacuk, ?The spaces Cp(X): Decomposition into a countable union of bounded subspaces and completeness properties,? Topol. Appl.,22, No. 3, 241?254 (1986). · Zbl 0596.54015 · doi:10.1016/0166-8641(86)90023-4
[356] V. V. Tkacuk, ?Approximation of RX with countable subsets of Cp(X) and calibers of the space Cp(X),? Comment. Math. Univ. Carol.,27, No. 2, 267?276 (1986).
[357] S. Todorcevic, ?Stationary sets, trees and continuums,? Publ. Inst. Math.,29, 249?262 (1981). · Zbl 0519.06002
[358] J. P. Troallic, ?Fonctions a valeurs dans des espaces fonctionnels generaux: theoremes de R. Ellis et de I. Namioka,? C. R. Acad. Sci.,AB287, No. 2, A63-A66 (1978). · Zbl 0394.54008
[359] J. P. Troallic, ?Espaces fonctionnels et theoremes de I. Namioka,? Bull. Soc. Math. France,107, No. 2, 127?137 (1979). · Zbl 0415.28017 · doi:10.24033/bsmf.1888
[360] V. V. Uspenskii, ?A characterization of real compactness in terms of the topology of pointwise convergence on the function spaces,? Comment. Math. Univ. Carol.,24, No. 1, 121?126 (1983).
[361] L. Vasak, ?On one generalization of weakly compactly generated Banach spaces,? Stud. Math. (PRL),70, No. 1, 11?19 (1981). · Zbl 0376.46012
[362] G. Vidossich, ?On topological spaces whose function space is of second category,? Invent. Math.,8, No. 2, 111?113 (1969). · Zbl 0176.19904 · doi:10.1007/BF01404614
[363] G. Vidossich, ?A remark on the density character of function spaces,? Proc. AMS,22, No. 3, 618?619 (1969). · Zbl 0181.25701 · doi:10.1090/S0002-9939-1969-0267521-9
[364] G. Vidossich, ?Characterizing separability of function spaces,? Invent. Math.,10, No. 3, 205?208 (1970). · Zbl 0189.53104 · doi:10.1007/BF01403249
[365] M. L. Wage, ?Weakly compact subsets of Banach spaces,? in: G. M. Reed, ed., Surveys in General Topology, Academic Press, NY (1980), pp. 479?494. · Zbl 0445.54009
[366] S. Warner, ?The topology of compact convergence of continuous function spaces,? Duke Math. J.,25, No. 2, 265?282 (1958). · Zbl 0081.32802 · doi:10.1215/S0012-7094-58-02523-7
[367] R. F. Wheeler, ?Weak and pointwise compactness in the space of bounded continuous functions,? Trans. AMS,266, No. 2, 515?530 (1981). · Zbl 0477.46016 · doi:10.1090/S0002-9947-1981-0617548-X
[368] M. de Wilde, ?Pointwise compactness in spaces of functions and R. C. James’ theorem,? Math. Ann.,208, 347 (1974). · Zbl 0274.46019
[369] O. Wyler, ?On the categories of general topology and topological algebra,? Arch. Math.,22, No. 1, 7?17 (1971). · Zbl 0265.18008 · doi:10.1007/BF01222531
[370] N. N. Yakovlev, ?On bicompacta in ?-products and related spaces,? Comment. Math. Univ. Carol.,21, No. 2, 263?283 (1980). · Zbl 0436.54019
[371] Ph. Zenor, ?Hereditary m-separability and the hereditary m-Lindelöf property in product spaces and function spaces,? Fund. Math.,106, 175?180 (1980). · Zbl 0454.54011
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