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Special issue on \(C_p(X)\)-theory. (English) Zbl 0922.00006

The articles of this volume will be reviewed individually.

MSC:

00B15 Collections of articles of miscellaneous specific interest
54-06 Proceedings, conferences, collections, etc. pertaining to general topology

Keywords:

Special issue
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References:

[1] Aharoni, I.; Lindenstrauss, J., Uniform equivalence between Banach spaces, Bull. Amer. Math. Soc., 84, 281-283 (1978) · Zbl 0401.57026
[2] Alster, K., Some remarks on Eberlein compacts, Fund. Math., 104, 43-46 (1979) · Zbl 0339.54022
[3] Alster, K.; Pol, R., On function spaces of compact subspaces of Σ-products of the real line, Fund. Math., 107, 135-143 (1980) · Zbl 0353.54007
[4] Amir, D.; Lindenstrauss, J., The structure of weakly compact sets in Banach spaces, Ann. of Math., 88, 1, 35-46 (1968) · Zbl 0164.14903
[5] Anderson, B. D., Projections and extension maps in \(C(T)\), Illinois J. Math., 17, 513-517 (1973) · Zbl 0259.41021
[6] Arens, R., A topology of spaces of transformations, Ann. of Math., 47, 480-495 (1946) · Zbl 0060.39704
[7] Arens, R., Extension of functions on fully normal spaces, Pacific J. Math., 2, 11-22 (1952) · Zbl 0046.11801
[8] Arens, R.; Dugundji, J., Topologies for function spaces, Pacific J. Math., 1, 1, 5-13 (1951) · Zbl 0044.11801
[9] Argyros, S.; Farmaki, V., On the structure of weakly compact subsets of Hilbert spaces and applications to the geometry of Banach spaces, Trans. Amer. Math. Soc., 289, 409-427 (1985) · Zbl 0585.46010
[10] Argyros, S.; Mercourakis, S., On weakly Lindelöf Banach spaces, Rocky Mountain J. Math., 23, 395-446 (1993) · Zbl 0797.46009
[11] Argyros, S.; Mercourakis, S.; Negrepontis, S., Analytic properties of Corson-compact spaces, (Novak, J., General Topology and its Relations to Modern Analysis and Algebra 5, Proc. Fifth Prague Topol. Symp.. General Topology and its Relations to Modern Analysis and Algebra 5, Proc. Fifth Prague Topol. Symp., 1981 (1982), Heldermann: Heldermann Berlin), 12-23 · Zbl 0656.46014
[12] Argyros, S.; Negrepontis, S., On weakly \(K\)-countably determined spaces of continuous functions, (Proc. Amer. Math. Soc., 87 (1983)), 731-736 · Zbl 0509.54020
[13] Arhangel’skii, A. V., Some topological spaces that occur in functional analysis, Russian Math. Surveys, 31, 14-30 (1976) · Zbl 0358.46019
[14] Arhangel’skii, A. V., Function spaces in the topology of pointwise convergence, and compact sets, Russian Math. Surveys, 39, 5, 9-56 (1984) · Zbl 0568.54016
[15] Arhangel’skii, A. V., Continuous maps, factorization theorems, and function spaces, Trans. Moscow Math. Soc., 47, 1-22 (1985) · Zbl 0588.54018
[16] Arhangel’skii, A. V., A survey of \(C_p\)-theory, Questions Answers Gen. Topology, 5, 1-109 (1987) · Zbl 0634.54012
[17] Arhangel’skii, A. V., Spaces of mappings and rings of continuous functions, (Arhangel’skii, A. V., General Topology 3. General Topology 3, Encyclopedia of Mathematical Sciences, 51 (1995), Springer: Springer Berlin), 73-156 · Zbl 0826.00014
[18] Arhangel’skii, A. V., Hereditarily Lindelöf spaces of continuous functions, Moscow Univ. Math. Bull., 44, 3, 67-69 (1989) · Zbl 0714.54011
[19] Arhangel’skii, A. V., On linear homeomorphism of function spaces, Soviet Math. Dokl., 25, 2, 852-855 (1982) · Zbl 0522.54015
[20] Arhangel’skii, A. V., Functional tightness, \(Q\)-spaces, and τ-embeddings, Comment. Math. Univ. Carolin., 24, 1, 105-120 (1983) · Zbl 0528.54006
[21] Arhangel’skii, A. V., Spaces of functions and completeness type conditions, Vestnik. Moskov. Univ. Ser. Mat. Mekh., 6, 4-9 (1983)
[22] Arhangel’skii, A. V., Problems in \(C_p\)-theory, (van Mill, J.; Reed, G. M., Open Problems in Topology (1990), North-Holland: North-Holland Amsterdam), 603-615, Chapter 31 · Zbl 0718.54001
[23] Arhangel’skii, A. V., Topological function spaces, (Math. Appl., 78 (1992), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht), (transl. from Russian) · Zbl 0848.54016
[24] Arhangel’skii, A. V., On the Lindelöf degree of topological spaces of functions, and on embeddings into \(C_p(X)\), Moscow Univ. Math. Bull., 45, 5, 43-45 (1990) · Zbl 0716.54012
[25] Arhangel’skii, A. V., Hurewicz spaces, analytic sets, and fan-tightness of function spaces, Soviet Math. Dokl., 33, 2, 397-399 (1986) · Zbl 0606.54013
[26] Arhangel’skii, A. V., On linear topological classification of spaces of continuous functions in the topology of pointwise convergence, Math. USSR-Sb., 70, 1, 129-142 (1991) · Zbl 0733.46009
[27] Arhangel’skii, A. V., \(C_p\)-theory, (Hus̆ek, M.; van Mill, J., Recent Progress in General Topology (1992), North-Holland: North-Holland Amsterdam), 1-56, Chapter 1 · Zbl 0814.54009
[28] Arhangel’skii, A. V., On Lindelöf property and spread in \(C_p\)-theory, Topology Appl., 74, 1-3, 83-90 (1996) · Zbl 0865.54006
[29] Arhangel’skii, A. V., On spread and condensations, (Proc. Amer. Math. Soc., 124 (1996)), 3519-3527, (11) · Zbl 0858.54003
[30] Arhangel’skii, A. V., On a theorem of Grothendieck in \(C_p\)-theory, Topology Appl., 80, 21-41 (1997) · Zbl 0888.54018
[31] A.V. Arhangel’skii, On condensations of \(C_p\); A.V. Arhangel’skii, On condensations of \(C_p\)
[32] A.V. Arhangel’skii and J. Calbrix, A characterization of σ-compactness of a space \(XR^X\); A.V. Arhangel’skii and J. Calbrix, A characterization of σ-compactness of a space \(XR^X\) · Zbl 0992.54016
[33] Arhangel’skii, A. V.; Cioban, M. M., On continuous mappings of \(C_p\)-spaces and extenders, (Proc. Steklov Inst. Math., 212 (1996)), 28-31 · Zbl 0896.54005
[34] Arhangel’skii, A. V.; Choban, M. M., \(C_p(X)\) and some other functors in General Topology. Continuous extenders, (Adamek, J.; MacLane, S., Categorical Topology (1989), World Scientific: World Scientific London), 432-445
[35] A.V. Arhangel’skii and M.M. Čoban, The extension properties of Tychonoff spaces and generalized retracts, Compt. Rend. Acad. Bulg. Sci. 41 (12) 5-7.; A.V. Arhangel’skii and M.M. Čoban, The extension properties of Tychonoff spaces and generalized retracts, Compt. Rend. Acad. Bulg. Sci. 41 (12) 5-7. · Zbl 0675.54014
[36] A.V. Arhangel’skii and M.M. Čoban, On the position of a subspace in the whole space, Compt. Rend. Acad. Bulg. Sci. 43 (4) 13-15.; A.V. Arhangel’skii and M.M. Čoban, On the position of a subspace in the whole space, Compt. Rend. Acad. Bulg. Sci. 43 (4) 13-15. · Zbl 0731.54004
[37] Arhangel’skii, A. V.; Szeptycki, P. J., Tightness in compact subspaces of \(C_p\)-spaces, Houston J. Math., 23, 1, 1-7 (1997) · Zbl 0882.54013
[38] Arhangel’skii, A. V.; Tkachuk, V. V., Calibers and point-finite cellularity of the spaces \(C_p(X)\) and some questions of S. Gul’ko and M. Hušek, Topology Appl., 23, 65-74 (1986) · Zbl 0591.54023
[39] Arhangel’skii, A. V.; Uspenskij, V. V., On the cardinality of Lindelöf subspaces of function spaces, Comment. Math. Univ. Carolin., 27, 673-676 (1986) · Zbl 0602.54003
[40] Asanov, M. O., About the space of continuous functions, (Colloq. Math. Soc. Janos Bolyai, 41 (1983), North-Holland: North-Holland Amsterdam), 31-34 · Zbl 0592.54020
[41] Asanov, M. O.; Velichko, N. V., Compact sets in \(C_p(X)\), Comment. Math. Univ. Carolin., 22, 255-266 (1981) · Zbl 0491.54011
[42] Baars, J., A note on linear mappings between function spaces, Comment. Math. Univ. Carolin., 34, 4, 711-715 (1993) · Zbl 0787.54017
[43] Baars, J., Function spaces of first countable paracompact spaces, Bull. Polon. Acad. Sci. Math., 42, 29-35 (1994) · Zbl 0815.54014
[44] Baars, J.; Gladdines, H., On the linear invariance of Lindelöf numbers, Canad. Math. Bull., 39, 2, 129-137 (1996) · Zbl 0857.54017
[45] Baars, J.; Gladdines, H.; van Mill, J., Absorbing systems in infinite-dimensional manifolds, Topology Appl., 50, 2, 147-182 (1993) · Zbl 0794.57005
[46] Baars, J.; de Groot, J., An isomorphical classification of function spaces of zero-dimensional locally compact separable metric spaces, Comment. Math. Univ. Carolin., 29, 577-595 (1988) · Zbl 0684.54011
[47] Baars, J.; de Groot, J., On the ι-equivalence of metric spaces, Fund. Math., 137, 25-43 (1991) · Zbl 0769.54015
[48] Baars, J.; de Groot, J., On Topological and Linear Equivalence of Certain Function Spaces, (CWI Tract, 86 (1992), Centre for Mathematics and Computer Sciences: Centre for Mathematics and Computer Sciences Amsterdam) · Zbl 0755.54007
[49] Baars, J.; de Groot, J.; van Mill, J.; Pelant, J., An example of \(ℓ_p\)-equivalent spaces which are not \(ℓp^∗- equivalent\), (Proc. Amer. Math. Soc., 119 (1993)), 963-969 · Zbl 0787.54018
[50] Baars, J.; de Groot, J.; Pelant, J., Function spaces of completely metrizable spaces, Trans. Amer. Math. Soc., 340, 2, 871-879 (1993) · Zbl 0841.54012
[51] Baire, R., Sur les fonctions des variables rèelles, Ann. Mat. Pura Appl., 3, 3, 16-30 (1899) · JFM 30.0359.01
[52] T. Banakh and R. Cauty, Universalité forte pour les sous-essembles totalement bornés. Applications aux espaces \(C_p}X\); T. Banakh and R. Cauty, Universalité forte pour les sous-essembles totalement bornés. Applications aux espaces \(C_p}X\)
[53] Bartle, R. G.; Graves, L. M., Mappings between function spaces, Trans. Amer. Math. Soc., 72, 400-413 (1952) · Zbl 0047.10901
[54] Bartle, R. G., On compactness in functional analysis, Trans. Amer. Math. Soc., 79, 35-57 (1955) · Zbl 0064.35503
[55] Baskirov, A. I., Normality and bicompactness of spaces of mappings, Vestnik. Moskov. Univ. Ser. I Mat. Mekh., 3, 77-79 (1972) · Zbl 0238.54013
[56] Baturov, D. P., On subspaces of function spaces, Vestnik. Moskov. Univ. Ser. Mat. Mekh., 4, 66-69 (1987) · Zbl 0626.54002
[57] Baturov, D. P., Normality of dense subsets of function spaces, Vestnik. Moskov. Univ. Ser. I Mat. Mekh., 4, 63-65 (1988) · Zbl 0662.54010
[58] D.P. Baturov, Some properties of the weak topology of Banach spaces, Preprint.; D.P. Baturov, Some properties of the weak topology of Banach spaces, Preprint. · Zbl 0725.46011
[59] Benyamini, Y.; Rudin, M. E.; Wage, M., Continuous images of weakly compact subsets of Banach spaces, Pacific J. Math., 70, 2, 309-324 (1977) · Zbl 0374.46011
[60] Bessaga, C.; Pelczynski, A., Spaces of continuous functions, 4, Studia Math., 19, 53-62 (1960) · Zbl 0094.30303
[61] Blasco, J. L., On μ-spaces and \(k_R\)-spaces, (Proc. Amer. Math. Soc., 67 (1977)), 179-186 · Zbl 0365.54009
[62] Borges, C. J., On stratifiable spaces, Pacific J. Math., 17, 1, 1-16 (1966) · Zbl 0175.19802
[63] Borges, C. J., On function spaces of stratifiable spaces and compact spaces, (Proc. Amer. Math. Soc., 17 (1966)), 1074-1078 · Zbl 0175.19803
[64] Bourgain, J., Compact sets of first Baire class, Bull. Soc. Math. Belg., 29, 2, 135-142 (1977) · Zbl 0416.54009
[65] Bourgain, J., Some remarks on compact sets of first Baire class, Bull. Soc. Math. Belg., 30, 3-10 (1978) · Zbl 0414.54011
[66] Bourgain, J.; Fremlin, D. H.; Talagrand, M., Pointwise compact sets of Baire-measurable functions, Amer. J. Math., 100, 845-886 (1978) · Zbl 0413.54016
[67] Bourgain, J.; Talagrand, M., Compacite extremal, (Proc. Amer. Math. Soc., 80 (1980)), 68-70 · Zbl 0435.46016
[68] Bouziad, A., Jeux topologiques et points de continuite d’une application separement continue, C. R. Acad. Sci. Paris Ser. I, 310, 359-362 (1990) · Zbl 0701.90110
[69] Bouziad, A., Une classe d’espaces co-Namioka, C. R. Acad. Sci. Paris, 310, 779-782 (1990) · Zbl 0706.54024
[70] Bouziad, A., Notes sur la propriete de Namioka, Trans. Amer. Math. Soc., 344, 2, 873-883 (1994) · Zbl 0836.54009
[71] Bouziad, A., The class of co-Namioka spaces is stable under product, (Proc. Amer. Math. Soc., 123 (1996)), 983-986 · Zbl 0844.54016
[72] Brown, R., Function spaces and product topologies, Oxford J. Math., 15, 2, 238-250 (1964) · Zbl 0126.38503
[73] Buchwalter, H.; Schmets, J., Sur quelques proprietes de l’espace \(C_s(T)\), J. Math. Pures Appl. Ser., 52, 3, 337-352 (1973), (9) · Zbl 0268.46025
[74] Burke, D. K.; Lutzer, D. J., Recent advances in the theory of generalized metric spaces, (Topology: Proceedings of the Memphis State University Conference. Topology: Proceedings of the Memphis State University Conference, Lecture Notes in Pure Appl. Math. (1976), Marcel Dekker: Marcel Dekker New York), 1-70 · Zbl 0353.54020
[75] Calbrix, J., Classes de Baire et espaces d’applications continues, C. R. Acad. Sci. Paris 301 Ser. I, 16, 759-762 (1985) · Zbl 0581.54023
[76] Calbrix, J., Espaces \(K_σ\) et espaces des applications continues, Bull. Soc. Math. France, 113, 183-203 (1985) · Zbl 0581.54010
[77] Calbrix, J., Filtres sur les entiers et ensembles analytiques, C. R. Acad. Sci. Paris, 305, 109-111 (1987) · Zbl 0615.54027
[78] Calbrix, J., Filtres boreliens sur l’ensemble des entiers et espaces des applications continues, Rev. Roumaine Math. Pures Appl., 33, 655-661 (1988) · Zbl 0659.54009
[79] Calbrix, J., k-spaces and Borel filters on the set of integers, Trans. Amer. Math. Soc., 348, 2085-2090 (1996), (in French) · Zbl 0868.54019
[80] Calbrix, J.; Troallic, J., Applications separement continues, C. R. Acad. Sci. Paris, 288, 647-648 (1979) · Zbl 0421.54009
[81] Cauty, R., L’espace des fonctions continues d’un espace metrique denombrable, (Proc. Amer. Math. Soc., 113 (1991)), 493-501 · Zbl 0735.54008
[82] Cauty, R.; Dobrowolski, T.; Marciszewski, W., A contribution to the topological classification of the spaces \(C_p(X)\), Fund. Math., 142, 269-301 (1993) · Zbl 0813.54009
[83] Choban, M. M., General theorems on functional equivalence of topological spaces, Topology Appl., 89, 223-239 (1998), (this issue) · Zbl 0933.54020
[84] Christensen, J. P.R., Topology and Borel Structure (1974), North-Holland: North-Holland Amsterdam · Zbl 0273.28001
[85] Christensen, J. P.R., Joint continuity of separately continuous functions, (Proc. Amer. Math. Soc., 82 (1981)), 455-461, (3) · Zbl 0472.54007
[86] Cieselski, K.; Pol, R., A weakly Lindelöf function space \(C(K)\) without any continuous injection into \(c_0(Γ)\), Bull. Acad. Polon. Sci., 32, 681-688 (1984) · Zbl 0571.54014
[87] Comfort, W. W.; Hager, A. W., Estimates for the number of real-valued continuous functions, Trans. Amer. Math. Soc., 150, 619-631 (1970) · Zbl 0199.57504
[88] Corson, H. H., Normality in subsets of product spaces, Amer. J. Math., 81, 785-796 (1959) · Zbl 0095.37302
[89] Corson, H. H., The weak topology of a Banach space, Trans. Amer. Math. Soc., 101, 1-15 (1961) · Zbl 0104.08502
[90] Corson, H. H.; Lindenstrauss, J., On function spaces which are Lindelöf spaces, Trans. Amer. Math. Soc., 121, 2, 479-491 (1966) · Zbl 0144.37102
[91] Debs, G., Espaces \(K\)-analytiques et espaces de Baire de fonctions continues, Mathematika, 32, 218-228 (1985) · Zbl 0603.46033
[92] Debs, G., Pointwise and uniform convergence on a Corson compact space, Topology Appl., 23, 299-303 (1986) · Zbl 0613.54007
[93] Deville, R., Convergence ponctuelle et uniforme sur un espace compact, Bull. Acad. Polon. Sci. Math., 37, 7-12 (1989) · Zbl 0759.54002
[94] Deville, R.; Godefroy, G., Some applications of projectional resolutions of identity, (Proc. London Math. Soc. Ser., 67 (1993)), 183-199, (1) · Zbl 0798.46008
[95] Dijkstra, J.; Dobrowolski, T.; Marciszewski, W.; van Mill, J.; Mogilski, J., Recent classification and characterization results in geometric topology, Bull. Amer. Math. Soc., 22, 2, 277-283 (1990) · Zbl 0713.57011
[96] Dijkstra, J.; Grilliot, T.; Lutzer, D.; van Mill, J., Function spaces of low Borel complexity, (Proc. Amer. Math. Soc., 94 (1985)), 703-710, (4) · Zbl 0525.54010
[97] Dijkstra, J.; Mogilski, J., The ambient homeomorphy of certain function spaces and sequence spaces, Comment. Math. Univ. Carolin., 37, 3, 595-611 (1996) · Zbl 0881.57018
[98] Dimov, G., Espaces d’Eberlein et espaces de types voisins, C. R. Acad. Sci. Paris Ser. I, 304, 9, 233-235 (1987) · Zbl 0605.54018
[99] G. Dimov, Baire subspaces of \(c_0ΓG_δ\); G. Dimov, Baire subspaces of \(c_0ΓG_δ\)
[100] G. Dimov and G. Tironi, Some remarks on almost radiality in function spaces, Preprint.; G. Dimov and G. Tironi, Some remarks on almost radiality in function spaces, Preprint. · Zbl 0673.46013
[101] Dobrowolski, T.; Gulko, S. P.; Mogilski, J., Function spaces homeomorphic to the countable product of \(ℓ_f^2\), Topology Appl., 34, 153-160 (1990) · Zbl 0691.57009
[102] Dobrowol’skij, T.; Marciszewski, W., Classification of function spaces with the pointwise topology determined by a countable dense set, Fund Math., 148, 35-62 (1995) · Zbl 0834.46016
[103] Dobrowolski, T.; Marciszewski, W.; Mogilski, J., Topological classification of function spaces \(C_p(X)\) of low Borel complexity, Trans. Amer. Math. Soc., 328, 307-324 (1991) · Zbl 0768.54016
[104] Dobrowolski, T.; Mogilski, J., Certain sequence and function spaces homeomorphic to the countable product of \(l_f^2\), J. London Math. Soc., 45, 2, 566-576 (1992) · Zbl 0783.46009
[105] van Douwen, E. K., Simultaneous extension of continuous functions, (PhD Dissertation (1975), Free University: Free University Amsterdam), 99
[106] van Douwen, E. K., Simultaneous linear extension of continuous functions, Gen. Topology Appl., 5, 297-319 (1975) · Zbl 0309.54013
[107] A. Dow, H. Junnila and J. Pelant, Weak covering properties of weak topologies, to appear.; A. Dow, H. Junnila and J. Pelant, Weak covering properties of weak topologies, to appear. · Zbl 0886.54014
[108] Dranishnikov, A. N., Absolytnye \(F\)-znachnye retrakty i prostranstva funktcij v topologii potochechnoj shodimosti, Sibirsk. Mat. Zh., 27, 74-86 (1986)
[109] Dugundji, J., An extension of Tietze’s theorem, Pacific J. Math., 1, 353-367 (1951) · Zbl 0043.38105
[110] Eberlein, W. F., Weak compactness in Banach spaces, (Proc. Nat. Acad. Sci. USA, 33 (1947)), 51-53 · Zbl 0029.26902
[111] Floret, K., Weakly Compact Sets, (Lecture Notes in Math., 801 (1980), Springer: Springer Berlin) · Zbl 0232.46004
[112] Fort, M. K., A note on pointwise convergence, (Proc. Amer. Math. Soc., 2 (1951)), 34-35 · Zbl 0043.11303
[113] Fox, R. H., On topologies for function spaces, Bull. Amer. Math. Soc., 51, 429-432 (1945) · Zbl 0060.41202
[114] Fuller, R. V., Condition for a function space to be locally compact, (Proc. Amer. Math. Soc., 36 (1972)), 615-617 · Zbl 0264.54009
[115] Gale, D., Compact sets of functions and function rings, (Proc. Amer. Math. Soc., 1 (1950)), 303-308 · Zbl 0037.35501
[116] Garcia-Ferreira, S.; Tamariz-Mascarua, A., \(p- Fréchet-Urysohn\) property of function spaces, Topology Appl., 58, 2, 157-172 (1994) · Zbl 0814.54011
[117] Gerlits, J., Some properties of \(C(X), 2\), Topology Appl., 15, 255-262 (1983) · Zbl 0505.54017
[118] Gerlits, J.; Nagy, Z., Some properties of \(C(X), 1\), Topology Appl., 14, 151-161 (1982) · Zbl 0503.54020
[119] Gerlits, J.; Nagy, Zs.; Szentmiklossy, Z., Some convergence properties in function spaces, (Frolik, Z., General Topology and its Relation to Modern Analysis and Algebra (1988), Heldermann: Heldermann Berlin), 211-222 · Zbl 0642.54013
[120] Gillespie, D. C.; Hurwitz, W. A., On sequences of continuous functions having continuous limits, Trans. Amer. Math. Soc., 32, 527-543 (1930) · JFM 56.0212.03
[121] Gillman, L.; Jerison, M., Rings of Continuous Functions (1960), Princeton · Zbl 0093.30001
[122] Godefroy, G., Compacts de Rosenthal, Pacific J. Math., 91, 293-306 (1980) · Zbl 0475.46003
[123] Godefroy, G.; Talagrand, M., Espaces de Banach representables, Israel J. Math., 41, 321-330 (1982) · Zbl 0498.46016
[124] Gordienko, I. Ju., Two theorems on relative cardinal invariants in \(C_p\)-theory, Zb. Rad. Filozofskog Fak. Nišu, Ser Mat., 4, 5-7 (1990)
[125] Grothendieck, A., Critéres de compacite dans les espaces fonctionnels généraux, Amer. J. Math., 74, 168-186 (1952) · Zbl 0046.11702
[126] Grothendieck, A., Sur les applications lineaires faiblement compactes d’espaces du type \(C(K)\), Canad. J. Math., 5, 129-173 (1953) · Zbl 0050.10902
[127] Gruenhage, G., Covering properties of \(X^2/ sbΔ W\)-sets, and compact subsets of Σ-products, Topology Appl., 17, 287-304 (1984) · Zbl 0547.54016
[128] Gruenhage, G., On a Corson compact space of Todorcevic, Fund. Math., 126, 261-268 (1986) · Zbl 0618.54021
[129] Gruenhage, G., Games, covering properties and Eberlein compacta, Topology Appl., 23, 291-298 (1986) · Zbl 0604.54022
[130] Gruenhage, G., A note on Gul’ko compact spaces, (Proc. Amer. Math. Soc., 100 (1987)), 371-376 · Zbl 0622.54020
[131] G. Gruenhage and D.K. Ma, Baireness of \(C_kXX\); G. Gruenhage and D.K. Ma, Baireness of \(C_kXX\) · Zbl 0886.54013
[132] Gul’ko, S. P., On properties of subsets of Σ-products, Soviet Math. Dokl., 18, 1438-1442 (1977) · Zbl 0397.54012
[133] Gul’ko, S. P., On properties of some function spaces, Soviet Math. Dokl., 19, 1420-1424 (1978) · Zbl 0421.54013
[134] Gul’ko, S. P., On the structure of spaces of continuous functions and on hereditary paracompactness of these spaces, Uspekhi Mat. Nauk, 34, 6, 33-40 (1979) · Zbl 0446.46014
[135] Gul’ko, S. P., On properties of function spaces, (Alexandroff, P. S., Seminar on General Topology (1981), Moscow State University: Moscow State University Moscow), 8-41 · Zbl 0823.46017
[136] Gul’ko, S. P., The space \(C_p(X)\) for countable infinite compact \(X\) is uniformly homeomorphic to \(c_0\), Bull. Acad. Polon. Sci., 36, 5, 391-396 (1988), 6 · Zbl 0754.54010
[137] Gul’ko, S. P., Spaces of continuous functions on ordinals and ultrafilters, Mat. Zametki, 47, 4, 26-34 (1990) · Zbl 0823.46017
[138] Gul’ko, S. P., Uniformly homeomorphic spaces of functions, (Proc. Steklov Inst. Math., 3 (1993)), 87-93
[139] Gul’ko, S. P.; Khmyleva, T. E., Compactness is not preserved by the relation of \(t\)-equivalence, Math. Notes, 39, 5, 484-488 (1986), 6 · Zbl 0629.54007
[140] Gul’ko, S. P.; Okunev, O. G., Local compactness and \(M\)-equivalence, (Ivanov, A. V.; etal., Questions of Geometry and Topology (1986), Petrozavodsk State University: Petrozavodsk State University Petrozavodsk), 14-23, (in Russian)
[141] Gul’ko, S. P.; Os’kin, A. V., Isomorphic classification of spaces of continuous functions on well ordered bicompacta, Funktsional. Anal. i Prilozhen., 9, 1, 61-62 (1975) · Zbl 0325.46039
[142] Guthrie, J. A., Mapping spaces and cs-networks, Pacific J. Math., 47, 465-471 (1973) · Zbl 0253.54025
[143] Guthrie, J. A., Ascoli theorems and the pseudocharacter of mapping spaces, Bull. Austral. Math. Soc., 10, 403-408 (1974) · Zbl 0284.54008
[144] Hager, A. W., Approximation of real continuous functions on Lindelöf spaces, (Proc. Amer. Math. Soc., 22 (1969)), 156-163 · Zbl 0175.42103
[145] Hansard, J. D., Function space topologies, Pacific J. Math., 35, 381-388 (1970) · Zbl 0185.50602
[146] Hansel, G.; Troallic, J. P., Quasicontinuity and Namioka’s theorem, Topology Appl., 46, 135-149 (1992) · Zbl 0812.54019
[147] Haydon, R. G., Compactness in \(C_s(T)\) and applications, Publ. Dép. Math. Lyon, 9, 1, 105-113 (1972)
[148] Haydon, R. G., On dual \(L^1\)-spaces and injective bidual Banach spaces, Israel J. Math., 31, 142-152 (1978) · Zbl 0407.46018
[149] Haydon, R. G., Some problems about scattered spaces, (Seminaire Initiation a l’Analyse. Seminaire Initiation a l’Analyse, J. Saint Raymond 29e Annee, 9 (1989/1990)), 10, G. Choquet, G. Godefroy, M. Rogalski · Zbl 0757.46009
[150] Haydon, R. G., A counterexample to several questions about scattered compact spaces, Bull. London Math. Soc., 22, 261-268 (1990) · Zbl 0725.46007
[151] Haydon, R. G., Countable unions of compact sets with the Namioka property, Mathematika, 41, 141-144 (1994) · Zbl 0812.54025
[152] Haydon, R. G., Baire trees, bad norms and the Namioka property, Mathematika, 42, 30-42 (1995) · Zbl 0870.46008
[153] Haydon, R. G.; Rogers, C. A., A locally uniformly convex renorming for certain \(C(K)\), Mathematika, 37, 1-8 (1990) · Zbl 0725.46008
[154] Heath, R. W., Monotonically normal spaces, Trans. Amer. Math. Soc., 178, 481-493 (1973) · Zbl 0269.54009
[155] Heath, R. W., Some comments on simultaneous extensions of mappings on closed subsets, (Topology Conference, VPI 375 (1973), Springer: Springer Berlin), 114-119 · Zbl 0287.54038
[156] Heath, R. W., Extension Properties of Generalized Metric Spaces, ((1977), Univ. North Carolina: Univ. North Carolina Greensboro), 1-46
[157] Heath, R. W.; Lutzer, D. J., The Dugundji extension theorem and collectionwise normality, Bull. Polon. Acad. Sci. Ser. Math., 22, 827-830 (1974) · Zbl 0297.54013
[158] R.W. Heath and D.J. Lutzer, Dugundji extension theorem for linearly ordered spaces, Pacific J. Math.; R.W. Heath and D.J. Lutzer, Dugundji extension theorem for linearly ordered spaces, Pacific J. Math. · Zbl 0302.54017
[159] Heath, R. W.; Lutzer, D. J.; Zenor, P. L., On continuous extenders, (Studies in Topology (1975), Academic Press: Academic Press New York), 203-213 · Zbl 0312.54021
[160] Helmer, D., Criteria for Eberlein compactness in spaces of continuous functions, Manuscripta Math., 35, 27-51 (1981) · Zbl 0476.46010
[161] Jayne, J. E., Spaces of Baire functions 1, Ann. Inst. Fourier, 24, 4, 47-76 (1974) · Zbl 0287.46031
[162] Jayne, J. E.; Namioka, I.; Rogers, C. A., Norm fragmented weak-star compact sets, Collect. Math., 41, 133-163 (1990) · Zbl 0764.46015
[163] Jayne, J. E.; Namioka, I.; Rogers, C. A., σ-fragmentable Banach spaces, Mathematika, 39, 161-188 (1992) · Zbl 0761.46008
[164] Kadec, M. I., A proof of topological equivalence of all separable infinite-dimensional Banach spaces, Funktsional. Anal. i Prilozhen., 1, 53-62 (1967)
[165] Kalamidas, N. D., Chain condition and continuous mappings on \(C_p(X)\), Rend. Sem. Mat. Univ. Padova, 87, 19-27 (1992) · Zbl 0767.54003
[166] Kalamidas, N. D.; Spiliopoulos, G. D., Compact sets in \(C_p(X)\) and calibers, Canad. Math. Bull., 35, 4, 497-502 (1992) · Zbl 0764.54008
[167] Kaul, S. K., Compact subsets in function spaces, Bull. Canad. Math., 12, 461-466 (1969) · Zbl 0184.47801
[168] Kawamura, K.; Morishita, K., Linear topological classification of certain function spaces on manifolds and CW, Topology Appl., 69, 3, 265-282 (1996) · Zbl 0855.46014
[169] Kenderov, P. S., Dense strong continuity of pointwise continuous mappings, Pacific J. Math., 89, 111-130 (1980) · Zbl 0458.54011
[170] Kenderov, P. S., \(C(T)\) is weak Asplund for every Gul’ko compact \(T\), C. R. Acad. Bulg. Sci., 40, 2, 17-19 (1987) · Zbl 0616.46010
[171] Khurana, S. S., Pointwise compactness on extreme points, (Proc. Amer. Math. Soc., 83 (1981)), 347-348 · Zbl 0467.46014
[172] Kislyakov, S. V., Isomorphic classification of spaces of continuous functions on ordinals, Sibirsk. Mat. Zh., 16, 3, 293-300 (1975) · Zbl 0327.46033
[173] Korovin, A. V., Continuous actions of pseudocompact groups and axioms of topological groups, Comment. Math. Univ. Carolin., 33, 335-343 (1992) · Zbl 0786.22002
[174] Koyama, A.; Okada, T., On compacta which are \(l\)-equivalent to \(I^n\), Tsukuba J. Math., 11, 1, 147-156 (1987) · Zbl 0641.54009
[175] Krivoruchko, A. I., On the cardinality of the set of continuous functions, Soviet Math. Dokl., 13, 1364-1367 (1972) · Zbl 0264.54003
[176] Krivoruchko, A. I., On cardinal invariants of spaces and mappings, Soviet Math. Dokl., 14, 1642-1647 (1973) · Zbl 0291.54005
[177] Krivoruchko, A. I., The cardinality and density of spaces of mappings, Soviet Math. Dokl., 16, 281-285 (1975) · Zbl 0339.54006
[178] Lambrinos, P., The bounded-open topology on function spaces, Manuscripta Math., 36, 47-66 (1981) · Zbl 0459.54011
[179] Lee, J. P.; Piotrowski, Z., A note on spaces related to Namioka spaces, Bull. Austral. Math. Soc., 31, 285-292 (1985) · Zbl 0549.54009
[180] Leiderman, A. G., On dense metrizable subspaces of Corson compacta, Mat. Zametki, 38, 440-449 (1985) · Zbl 0602.54024
[181] Leiderman, A. G., Adequate families of sets and function spaces, Comment. Math. Univ. Carolin., 29, 1, 31-39 (1988) · Zbl 0653.54012
[182] Leiderman, A. G.; Malykhin, V. I., On nonpreservation of final compactness by products of spaces \(C_p(X)\), Sibirsk. Mat. Zh., 29, 1, 84-93 (1988) · Zbl 0653.54011
[183] A.G. Leiderman, S.A. Morris and V.G. Pestov, The free Abelian topological group and the free locally convex space on the unit interval, Preprint.; A.G. Leiderman, S.A. Morris and V.G. Pestov, The free Abelian topological group and the free locally convex space on the unit interval, Preprint. · Zbl 0907.22002
[184] Leiderman, A. G.; Sokolov, G. A., Adequate families of sets and Corson compacts, Comment. Math. Univ. Carolin., 25, 233-246 (1984) · Zbl 0586.54022
[185] Lindenstrauss, J., Weakly compact sets—their topological properties and the Banach spaces they generate, (Ann. of Math. Studies, 69 (1972), Princeton Univ. Press), 235-273 · Zbl 0232.46019
[186] Lindenstrauss, J.; Stegall, C., Examples of separable spaces which do not contain \(ℓ^1\) and whose duals are nonseparable, Studia Math., 54, 81-105 (1975) · Zbl 0324.46017
[187] Lindenstrauss, J.; Tzafriri, L., Classical Banach Spaces I (1977), Springer: Springer Berlin · Zbl 0362.46013
[188] Lutzer, D. J.; McCoy, R. A., Category in function spaces, Pacific J. Math., 90, 145-168 (1980) · Zbl 0481.54017
[189] Lutzer, D. J.; van Mill, J.; Pol, R., Descriptive complexity of function spaces, Trans. Amer. Math. Soc., 291, 121-128 (1985) · Zbl 0574.54042
[190] Ma, D. K., The Cantor tree, the γ-property, and Baire function spaces, (Proc. Amer. Math. Soc., 119 (1993)), 903-913, (3) · Zbl 0785.54019
[191] Malykhin, V. I., Spaces of continuous functions in simplest generic extensions, Math. Notes, 41, 301-304 (1987) · Zbl 0632.54003
[192] Malykhin, V. I.; Shakhmatov, D. B., Cartesian products of Fréchet topological groups and function spaces, Acta Math. Hungar., 60, 207-215 (1992) · Zbl 0764.54016
[193] Marciszewski, W., Lindelöf property in function spaces and a related selection theorem, (Proc. Amer. Math. Soc., 101 (1987)), 545-550 · Zbl 0627.54006
[194] Marciszewski, W., A function space \(C(K)\) not weakly homeomorphic to \(C(K) × C(K)\), Studia Math., 88, 129-137 (1988) · Zbl 0666.46022
[195] Marciszewski, W., Order types, calibers and spread of Corson compacta, Topology Appl., 42, 291-299 (1991) · Zbl 0768.54001
[196] Marciszewski, W., On universal Borel and projective filters, Bull. Polon. Acad. Sci. Math., 43, 1, 41-45 (1995) · Zbl 0824.04001
[197] Marciszewski, W., A countable \(X\) having a closed subspace \(A\) with \(C_p(A)\) not a factor of \(C_p(X)\), Topology Appl., 64, 141-147 (1995) · Zbl 0823.54011
[198] Marciszewski, W., On a classification of pointwise compact sets of the first Baire class functions, Fund. Math., 133, 195-209 (1989) · Zbl 0719.54022
[199] Marciszewski, W., On properties of Rosenthal compacta, (Proc. Amer. Math. Soc., 115 (1992)), 797-805 · Zbl 0790.54017
[200] Marciszewski, W., On analytic and coanalytic function spaces \(C_p(X)\), Topology Appl., 50, 241-248 (1993) · Zbl 0785.54020
[201] Marciszewski, W., On sequential convergence in weakly compact subsets of Banach spaces, Studia Math., 112, 2, 189-194 (1995) · Zbl 0822.46004
[202] Marciszewski, W., \(P\)-filters and hereditary Baire function spaces, Topology Appl., 89, 241-247 (1998), (this issue) · Zbl 0969.54016
[203] Marciszewski, W., A function space \(C_p(X)\) not linearly homeomorphic to \(C_p(X)\) × \(R\), Topology Appl., 89, 241-247 (1998), (this issue) · Zbl 0969.54016
[204] Marciszewski, W.; Pelant, J., Absolute Borel sets and function spaces, (Fac. Wiskunde en Informatica, Rapport WS-447 (1995), Vrije Universiteit: Vrije Universiteit Amsterdam), 1-16
[205] McCoy, R. A., First category function spaces under the topology of pointwise convergence, (Proc. Amer. Math. Soc., 50 (1975)), 431-434 · Zbl 0278.54013
[206] McCoy, R. A., Characterization of pseudocompactness by the topology of uniform convergence on function spaces, J. Austral. Math. Soc., 26, 251-256 (1978) · Zbl 0396.54006
[207] McCoy, R. A., Submetrizable spaces and almost σ-compact function spaces, (Proc. Amer. Math. Soc., 71 (1978)), 138-142 · Zbl 0388.54012
[208] McCoy, R. A., Countability properties of function spaces, Rocky Mountain J. Math., 10, 717-730 (1980) · Zbl 0431.54008
[209] McCoy, R. A., Necessary conditions for function spaces to be Lindelöf, Glas. Mat., 15, 163-168 (1980) · Zbl 0438.54011
[210] McCoy, R. A., Function spaces which are \(k\)-spaces, (Topology Proc., 5 (1980)), 139-146 · Zbl 0461.54011
[211] McCoy, R. A., A \(K\)-space function spaces, Int. J. Math. Sci., 3, 701-711 (1980) · Zbl 0449.54013
[212] McCoy, R. A.; Ntantu, I., Topological Properties of Spaces of Continuous Functions, (Lectures Notes in Math., 1315 (1988), Springer: Springer Berlin) · Zbl 0621.54011
[213] McCoy, R. A.; Ntantu, I., Completeness properties of function spaces, Topology Appl., 22, 191-206 (1986) · Zbl 0621.54011
[214] Mercourakis, S.; Negrepontis, S., Banach spaces and Topology 2, (Hušek, M.; van Mill, J., Recent Progress in Topology (1992), Elsevier: Elsevier New York) · Zbl 0656.46014
[215] Meyer, P. R., Function spaces and the Aleksandrov-Urysohn conjecture, Estratto degli Annali di Matematica Pura ed Applicata Ser. 4, 86, 25-29 (1970)
[216] Michael, E., On a theorem of Rudin and Klee, (Proc. Amer. Math. Soc., 12 (1961)), 921 · Zbl 0104.39301
[217] Michael, E., \(ℵ0- spaces\), J. Math. Mech., 15, 983-1002 (1966) · Zbl 0148.16701
[218] Michael, E., Paracompactness and the Lindelöf property in finite and countable Cartesian products, Compositio Math., 23, 179-214 (1971) · Zbl 0216.44304
[219] Michael, E., \(ℵ0- spaces\) and a function space theorem of R. Pol, Indiana Univ. Math. J., 26, 299-306 (1977) · Zbl 0352.54010
[220] Michael, E. A.; Rudin, M. E., A note on Eberlein compacts, Pacific J. Math., 72, 2, 487-495 (1977) · Zbl 0345.54020
[221] Michael, E. A.; Rudin, M. E., Another note on Eberlein compacts, Pacific J. Math., 72, 2, 497-499 (1977) · Zbl 0344.54018
[222] van Mill, J., Infinite-Dimensional Topology. Prerequisites and Introduction (1989), North-Holland: North-Holland Amsterdam · Zbl 0663.57001
[223] van Mill, J., Topological equivalence of certain function spaces, Compositio Math., 63, 159-188 (1987) · Zbl 0634.54011
[224] van Mill, J.; Pol, R., A countable space with a closed subspace without measurable extender, Bull. Acad. Polon. Sci., 41, 279-283 (1993) · Zbl 0839.54019
[225] K. Morishita, The \(k_R\); K. Morishita, The \(k_R\)
[226] Morita, K., Note on mapping spaces, (Proc. Japan Acad., 32 (1956)), 671-675 · Zbl 0072.40403
[227] Nachbin, L., Topological vector spaces of continuous functions, (Proc. Nat. Acad. Sci. USA, 40 (1954)), 471-474 · Zbl 0055.09803
[228] Nagata, J., On lattices of functions on topological spaces and of functions on uniform spaces, Osaka Math. J., 1, 2, 166-181 (1949) · Zbl 0036.38602
[229] L.B. Nahmanson, Lindelöf property of function spaces, Preprint.; L.B. Nahmanson, Lindelöf property of function spaces, Preprint.
[230] Namioka, I., Separate continuity and joint continuity, Pacific J. Math., 51, 515-531 (1974) · Zbl 0294.54010
[231] Namioka, I., Radon-Nicodym compact spaces and fragmentability, Mathematika, 34, 258-281 (1987) · Zbl 0654.46017
[232] Namioka, I.; Phelps, R. R., Banach spaces which are Asplund spaces, Duke Math. J., 42, 735-750 (1975) · Zbl 0332.46013
[233] Namioka, I.; Pol, R., Mappings of Baire spaces into function spaces and Kadeč renorming, Israel J. Math., 78, 1-20 (1992) · Zbl 0794.54036
[234] Negrepontis, S., Banach spaces and topology, (Handbook of Set-Theoretic Topology (1984), North-Holland: North-Holland Amsterdam), 1001-1142 · Zbl 0584.46007
[235] Noble, N., The density character of function spaces, (Proc. Amer. Math. Soc., 42 (1974)), 228-233 · Zbl 0278.54016
[236] Nyikos, P., Classes of compact sequential spaces, (Set Theory and its Applications. Set Theory and its Applications, Lecture Notes in Math., 1401 (1989), Springer: Springer Berlin), 135-159 · Zbl 0697.54015
[237] Nyikos, P., Properties of Eberlein compacta, (Abstracts of Eighth Summer Conference on General Topology and Applications (1992)), 28
[238] Okada, T., A remark on Eberlein compacta, Kobe J. Math., 2, 65-66 (1985) · Zbl 0577.54021
[239] Okunev, O. G., On spaces of functions in the topology of pointwise convergence: Hewitt’s extension and τ-continuous functions, Vestnik. Moskov. Univ. Ser. Mat. Mech., 4, 78-80 (1985) · Zbl 0582.54010
[240] Okunev, O. G., Weak topology of an associated space, and \(t\)-equivalence, Math. Notes, 46, 1, 534-538 (1990), 2 · Zbl 0774.46020
[241] Okunev, O. G., On Lindelöf Σ-spaces of continuous functions in the pointwise topology, Topology Appl., 49, 149-166 (1993) · Zbl 0796.54026
[242] Okunev, O. G., On Lindelöf sets of continuous functions, Topology Appl., 63, 91-96 (1995) · Zbl 0823.54012
[243] Okunev, O. G., On analyticity in cosmic spaces, Comment. Math. Univ. Carolin., 34, 185-190 (1993) · Zbl 0837.54009
[244] O.G. Okunev, Homeomorphisms of function spaces and hereditary cardinal invariants, Topology Appl., to appear.; O.G. Okunev, Homeomorphisms of function spaces and hereditary cardinal invariants, Topology Appl., to appear. · Zbl 0892.54008
[245] Okuyama, A., Some relationships between function spaces and hyperspaces of compact sets, (Novac, J., General Topology and Rel. to Modern Anal. and Algebra V, Fifth PragueTopol. Symp. (1981)), 527-535 · Zbl 0509.54009
[246] O’Meara, P., Paracompactness in function spaces with the compact-open topology, (Proc. Amer. Math. Soc., 29 (1971)), 183-189 · Zbl 0214.21105
[247] Orihuela, J., Pointwise compactness in spaces of continuous functions, J. London Math. Soc., 36, 2, 143-152 (1987) · Zbl 0608.46007
[248] Orihuela, J.; Schachermayer, W.; Valdivia, M., Every Radon-Nikodym Corson compact space is Eberlein compact, Studia Math., 98, 2, 157-174 (1991) · Zbl 0771.46015
[249] Pavlovskij, D. S., Spaces of open sets and spaces of continuous functions, Soviet Math. Dokl., 20, 564-568 (1979) · Zbl 0428.54003
[250] Pavlovskij, D. S., On spaces of continuous functions, Dokl. Akad. Nauk SSSR, 253, 1, 38-41 (1980) · Zbl 0489.54011
[251] Pelant, J., A remark on spaces of bounded continuous functions, Indag. Math., 91, 335-338 (1988) · Zbl 0685.54010
[252] Pelczynski, A., Linear Extensions, Linear Averagings, and their Applications (1968), PWN: PWN Warsaw · Zbl 0165.14603
[253] Pelczynski, A.; Semadeni, Z., Spaces of continuous functions (3) (spaces \(C(Ω)\) for Ω) without perfect subsets, Studia Math., 18, 211-222 (1959) · Zbl 0091.27803
[254] Pestov, V. G., The coincidence of the dimension dim of \(l\)-equivalent topological spaces, Soviet Math. Dokl., 26, 380-383 (1982) · Zbl 0518.54030
[255] Piotrowski, Z., Separate and joint continuity, Real Anal. Exchange, 11, 293-322 (1985/1986) · Zbl 0606.54009
[256] Plebanek, G., Compact spaces that result from adequate families of sets, Topology Appl., 65, 3, 257-270 (1995) · Zbl 0869.54003
[257] Pol, R., Normality in function spaces, Fund. Math., 84, 145-155 (1974) · Zbl 0277.54008
[258] Pol, R., Concerning function spaces on separable compact spaces, Bull. Acad. Polon. Sci. Math., 25, 993-997 (1977) · Zbl 0389.54009
[259] Pol, R., The Lindelöf property and its convex analogue in function spaces with the weak topology, (Coll. Math. Soc. Janos Bolyai 23. Coll. Math. Soc. Janos Bolyai 23, Topology (1978)), 965-969, Budapest · Zbl 0437.54012
[260] Pol, R., A function space \(C(X)\) which is weakly Lindelöf but not weakly compactly generated, Studia Math., 64, 279-285 (1979) · Zbl 0424.46011
[261] Pol, R., On a question of H.H. Corson and some related problems, Fund. Math., 109, 143-154 (1980) · Zbl 0486.46007
[262] Pol, R., A theorem on the weak topology of \(C(X)\) for compact scattered \(X\), Fund. Math., 106, 135-140 (1980) · Zbl 0444.54010
[263] Pol, R., Note on the spaces \(P(S)\) of regular probability measures whose topology is determined by countable subsets, Pacific J. Math., 100, 185-201 (1982) · Zbl 0522.46019
[264] Pol, R., On Pointwise and Weak Topology in Function Spaces (1984), Warsaw University
[265] Pol, R., Note on compact sets of first Baire class functions, (Proc. Amer. Math. Soc., 96 (1986)), 152-154, (1) · Zbl 0584.54014
[266] Pol, R., Note on pointwise convergence of sequences of analytic sets, Mathematica, 36, 290-300 (1989) · Zbl 0719.54047
[267] Pol, R., For a metrizable \(X, C_p(X)\) need not be linearly homeomorphic to \(C_p(X)\) × \(C_p(X)\), Mathematika, 42, 49-55 (1995) · Zbl 0839.46016
[268] Preiss, D.; Simon, P., A weakly pseudocompact subspace of a Banach space is weakly compact, Comment. Math. Univ. Carolin., 15, 4, 603-609 (1974) · Zbl 0306.54033
[269] Pryce, J. D., A device of R.J. Whitley’s applied to pointwise compactness in spaces of continuous functions, (Proc. London Math. Soc., 23 (1971)), 532-546, (3) · Zbl 0221.46012
[270] Ptak, V., On a theorem of W.F. Eberlein, Studia Math., 14, 276-284 (1954) · Zbl 0065.09603
[271] Ptak, V., Weak compactness in convex topological vector spaces, Czechoslovak Math. J., 79, 175-186 (1954) · Zbl 0057.09402
[272] Ptak, V., Two remarks on weak compactness, Czechoslovak Math. J., 80, 532-545 (1955) · Zbl 0068.31604
[273] Ptak, V., A combinatorial lemma on the existence of convex means and its application to weak compactness, (Proc. Sympos. Pure Math.. Proc. Sympos. Pure Math., Convexity, 7 (1963)), 437-450 · Zbl 0144.16903
[274] Pytkeev, E. G., On sequentiality of spaces of continuous functions, Uspekhi Mat. Nauk, 37, 5, 197-198 (1982), (in Russian) · Zbl 0508.54011
[275] Pytkeev, E. G., On the tightness of spaces of continuous functions, Uspekhi Mat. Nauk, 37, 157-158 (1982), (in Russian) · Zbl 0501.54008
[276] Pytkeev, E. G., The Baire property of spaces of continuous functions, Mat. Zametki, 38, 726-740 (1985) · Zbl 0601.54032
[277] Rajagopalan, M.; Wheeler, R. F., Sequential compactness of \(X\) implies a completeness property for \(C(X)\), Canad. J. Math., 28, 207-210 (1976) · Zbl 0318.46033
[278] Reznichenko, E. A., Normality and collectionwise normality in function spaces, Moscow Univ. Math. Bull., 45, 6, 25-26 (1990) · Zbl 0739.46007
[279] Reznichenko, E. A., Extension of functions defined on products of pseudocompact spaces and continuity of the inverse in pseudocompact groups, Topology Appl., 59, 3, 233-244 (1994) · Zbl 0835.22001
[280] E.A. Reznichenko, On Corson compacta, Preprint (in Russian).; E.A. Reznichenko, On Corson compacta, Preprint (in Russian).
[281] Reynov, O. I., On a class of compacts and GSG Banach spaces, Studia Math., 71, 113-126 (1981) · Zbl 0415.46013
[282] Ribarska, N. K., Internal characterization of fragmentable spaces, Mathematika, 34, 243-257 (1987) · Zbl 0645.46017
[283] Rosenthal, H. P., The heredity problem for weakly compactly generated Banach spaces, Compositio Math., 28, 83-111 (1974) · Zbl 0298.46013
[284] Rosenthal, H. P., Pointwise compact subsets of the first Baire class, Amer. J. Math., 99, 362-378 (1977) · Zbl 0392.54009
[285] Rosenthal, H. P., Some recent discoveries in the isomorphic theory of Banach spaces, Bull. Amer. Math. Soc., 84, 803-831 (1978) · Zbl 0391.46016
[286] Rudin, M. E., A note on certain function spaces, Arch. Math., 7, 469-470 (1956) · Zbl 0077.16401
[287] Raymond, J. Saint, Fonctions boreliennes sur quotients, Bull. Sci. Math., 100, 2, 141-147 (1976) · Zbl 0336.54015
[288] Raymond, J. Saint, Jeux topologiques et espaces de Namioka, (Proc. Amer. Math. Soc., 87 (1984)), 499-504 · Zbl 0511.54007
[289] Sakai, M., On supertightness and function spaces, Comment. Math. Univ. Carolin., 29, 2, 249-251 (1988) · Zbl 0655.54002
[290] Sakai, M., On embeddings into \(C_p(X)\) where \(X\) is Lindelöf, Comment. Math. Univ. Carolin., 33, 1, 165-171 (1992) · Zbl 0788.54019
[291] M. Sakai, On calibers of function spaces, Preprint.; M. Sakai, On calibers of function spaces, Preprint.
[292] Semadeni, Z., Banach Spaces of Continuous Functions (1971), PWN: PWN Warszawa · Zbl 0117.33002
[293] Schachermayer, W., Eberlein compacts et espaces de Radon, C. R. Acad. Sci. Paris, 284, 405-407 (1977) · Zbl 0348.46015
[294] Schmets, J., Espaces de Fonctions Continues, (Lecture Notes in Math. (1976), Springer: Springer Berlin), 519 · Zbl 0334.46022
[295] Shakhmatov, D. B., A pseudocompact Tychonoff space all countable subsets of which are closed and \(C^∗- embedded\), Topology Appl., 22, 2, 139-144 (1986) · Zbl 0586.54020
[296] Shirota, T., On locally convex vector spaces of continuous functions, (Proc. Japan Acad., 30 (1954)), 294-298 · Zbl 0057.33801
[297] Simon, P., On continuous images of Eberlein compacts, Comment. Math. Univ. Carolin., 17, 179-194 (1976) · Zbl 0322.54014
[298] Sipacheva, O. V., Lindelöf Σ-spaces of functions and the Souslin number, Moscow Univ. Math. Bull., 43, 3, 21-24 (1988) · Zbl 0653.54009
[299] Sipacheva, O. V., On Lindelöf subspaces of function spaces over linearly ordered separable compacta, (General Topology, Spaces and Functions (1989), MGU: MGU Moscow), 143-148
[300] Sipacheva, O. V., The structure of iterated function spaces in the topology of pointwise convergence for Eberlein compacta, Mat. Zametki, 47, 3, 91-99 (1990) · Zbl 0717.54010
[301] Sokolov, G. A., Lindelöf spaces of continuous functions, Math. Notes, 39, 6, 480-484 (1986) · Zbl 0607.54012
[302] Sokolov, G. A., On some classes of compact spaces lying in Σ-products, Comment. Math. Univ. Carolin., 25, 219-231 (1984) · Zbl 0577.54014
[303] Sokolov, G. A., Lindelöf property and the iterated continuous function spaces, Fund. Math., 143, 87-95 (1993) · Zbl 0841.54011
[304] Stegall, C., The Radon-Nikodym property in conjugate Banach spaces, Trans. Amer. Math. Soc., 206, 213-223 (1975) · Zbl 0318.46056
[305] Stegall, C., Applications of Descriptive Topology in Functional Analysis (1985-1987), Linz University
[306] Stegall, C., Topological spaces with dense subspaces that are homeomorphic to complete metric spaces and the classification of \(C(K)\) Banach spaces, Mathematica, 34, 101-107 (1987) · Zbl 0644.46012
[307] Stegall, C., Generalizations of a theorem of Namioka, (Proc. Amer. Math. Soc., 102 (1988)), 559-564 · Zbl 0652.46014
[308] Stegall, C., The topology of certain spaces of measures, (Notas Mat., 3 (1988), Universidad de Murcia) · Zbl 0259.46016
[309] Stone, A. H., A note on paracompactness and normality of mapping spaces, (Proc. Amer. Math. Soc., 14 (1963)), 81-83 · Zbl 0118.18203
[310] A. Szymanski, On Namioka theorem, Preprint.; A. Szymanski, On Namioka theorem, Preprint.
[311] Talagrand, M., Sur une conjecture de H.H. Corson, Bull. Sci. Math., 99, 2, 211-212 (1975) · Zbl 0317.46017
[312] Talagrand, M., Comparison des boreliens d’un espace de Banach pour les topologies fortes et faibles, Indiana Univ. Math. J., 27, 1001-1004 (1978) · Zbl 0396.28007
[313] Talagrand, M., Ensembles K-analytiques et fonctions croissantes de compacts, (Seminaire Choquet. Seminaire Choquet, Communication, 1 (1977/1978)), 2 · Zbl 0392.54023
[314] Talagrand, M., Sur la K-analyticite de certains espaces d’operateurs, Israel J. Math., 32, 124-130 (1979) · Zbl 0395.46008
[315] Talagrand, M., Espaces de Banach faiblement K-analytiques, Ann. of Math., 110, 3, 407-438 (1979) · Zbl 0393.46019
[316] Talagrand, M., Deux generalizations d’un theoreme de I. Namioka, Pacific J. Math., 81, 239-251 (1979) · Zbl 0367.54004
[317] Talagrand, M., Compacts de fonctions mesurables et filtres non mesurables, Studia Math., 67, 13-43 (1980) · Zbl 0435.46023
[318] Talagrand, M., A new countably determined Banach space, Israel J. Math., 47, 75-80 (1984) · Zbl 0537.46019
[319] Talagrand, M., Espaces de Baire et espaces de Namioka, Math. Ann., 270, 159-164 (1985) · Zbl 0582.54008
[320] Tani, T., Perfectly finally compact spaces are hard, Math. Japonica, 24, 323-326 (1979) · Zbl 0432.54015
[321] Tkachenko, M. G., On continuous images of spaces of functions, Sibirsk. Mat. Zh., 26, 5, 159-167 (1985) · Zbl 0587.54005
[322] Tkachuk, V. V., Duality with respect to the \(C_p\)-functor and cardinal invariants of Souslin type, Mat. Zametki, 37, 3, 441-451 (1985) · Zbl 0568.54005
[323] Tkachuk, V. V., The spaces \(C_p(X)\): decomposition into a countable union of bounded subspaces and completeness properties, Topology Appl., 22, 3, 241-253 (1986) · Zbl 0596.54015
[324] Tkachuk, V. V., Calibers of spaces of functions and metrization problem for compact subsets of \(C_p(X)\), Vestnik. Moskov. Univ. Ser. I Mat. Mekh., 3, 21-24 (1988) · Zbl 0653.54010
[325] Tkachuk, V. V., On cardinal invariants of Souslin number type, Soviet Math. Dokl., 27, 3, 681-684 (1983) · Zbl 0539.54001
[326] Tkachuk, V. V., On a supertopological cardinal invariant, Vestnik. Moskov. Univ. Mat., 39, 4, 26-29 (1984) · Zbl 0562.54008
[327] Tkachuk, V. V., On multiplicativity of some properties of spaces of mappings in the topology of pointwise convergence, Vestnik. Moskov. Univ. Ser. Mat. Mekh., 6, 36-38 (1984) · Zbl 0577.54013
[328] Tkachuk, V. V., Duality with respect to \(C_p\)-functor, and cardinal invariants of Souslin type, Mat. Zametki, 37, 3, 441-451 (1985) · Zbl 0568.54005
[329] Tkachuk, V. V., Approximation of \(R^X\) with countable subsets of \(C_p(X)\) and calibers of the space \(C_p(X)\), Comment. Math. Univ. Carolin., 27, 2, 267-276 (1986) · Zbl 0601.54002
[330] Tkachuk, V. V., A characterization of the Baire property of \(C_p(X)\) by a property of \(X\), (Mappings and Extensions of Topological Spaces (1985), Ustinov), 21-27
[331] Tkachuk, V. V., Methods of the theory of cardinal invariants and the theory of mappings applied to the spaces of functions, Sibirsk. Mat. Zh., 32, 1, 116-130 (1991) · Zbl 0739.46008
[332] Tkachuk, V. V., What if \(C_p(X)\) is perfectly normal?, Topology Appl., 65, 57-67 (1995) · Zbl 0868.54002
[333] Tkachuk, V. V.; Shakhmatov, D. B., When is \(C_p(X)\) σ-countably compact?, Vestnik. Moskov. Univ. Ser. Mat. Mekh., 1, 70-72 (1986) · Zbl 0619.54009
[334] Todd, A. R., Pseudocompact sets, absolutely Warner bounded sets and continuous function spaces, Arch. Math., 56, 474-481 (1991) · Zbl 0697.46010
[335] Todorcevic, S., Some Applications of \(S\) and \(L\) Combinatorics, (The Work of Mary Ellen Rudin. The Work of Mary Ellen Rudin, Ann. New York Acad. Sci., 705 (1993)), 130-167 · Zbl 0836.54018
[336] S. Todorcevic, Compact sets of the first Baire class, Preprint.; S. Todorcevic, Compact sets of the first Baire class, Preprint. · Zbl 0938.26004
[337] Troallic, J. P., Espaces fonctionnels et theorems de Namioka, Bull. Soc. Math. France, 107, 127-137 (1979) · Zbl 0415.28017
[338] Troallic, J. P., Une approche nouvelle de la presque-periodicite faible, (Semigroup Forum, 22 (1981)), 247-255 · Zbl 0464.22003
[339] Troallic, J. P., Quasi-continuite, continuite separee et topologie extremale, (Proc. Amer. Math. Soc., 110 (1990)), 819-827 · Zbl 0704.54007
[340] Tulcea, A. I., On pointwise convergence, compactness and equicontinuity, Adv. Math., 12, 171-177 (1974) · Zbl 0301.46032
[341] Tychonoff, A., Uber einer Funktionenraum, Math. Ann., 111, 762-766 (1935) · JFM 61.1194.04
[342] Uspenskij, V. V., On embeddings into function spaces, Dokl. Akad. Nauk SSSR, 242, 3, 545-546 (1978)
[343] Uspenskij, V. V., A characterization of compactness in terms of the uniform structure in the space of functions, Uspekhi Mat. Nauk, 37, 4, 183-184 (1982) · Zbl 0531.54017
[344] Uspenskij, V. V., On the frequency spectrum of function spaces, Vestnik. Moskov. Univ. Ser. I Mat. Mekh., 31-35 (1982)
[345] Uspenskij, V. V., A characterization of realcompactness in terms of the topology of pointwise convergence on the function space, Comment. Math. Univ. Carolin., 24, 121-126 (1983) · Zbl 0528.54007
[346] Uspenskij, V. V., On the topology of free locally convex space, Soviet Math. Dokl., 27, 3, 781-785 (1983) · Zbl 0569.54015
[347] Valov, V. M., Some properties of \(C_p(X)\), Comment. Math. Univ. Carolin., 27, 4, 665-672 (1986) · Zbl 0602.54016
[348] Valov, V. M., Linear topological classification of certain function spaces, Trans. Amer. Math. Soc., 327, 2, 583-600 (1991) · Zbl 0769.46010
[349] Vašak, L., On one generalization of weakly compactly generated Banach spaces, Studia Math., 70, 11-19 (1980) · Zbl 0376.46012
[350] Velichko, N. V., The Lindelöf property is \(l\)-invariant, Topology Appl., 89, 277-283 (1998), (this issue) · Zbl 0923.54017
[351] Velichko, N. V., On the weak topology of spaces of continuous functions, Mat. Zametki, 30, 5, 703-712 (1981) · Zbl 0505.54016
[352] Vidossich, G., A remark on the density character of function spaces, (Proc. Amer. Math. Soc., 22 (1969)), 618-619 · Zbl 0181.25701
[353] Vidossich, G., On topological spaces whose function space is of second category, Invent. Math., 8, 111-113 (1969) · Zbl 0176.19904
[354] Vidossich, G., Characterizing separability of function spaces, Invent. Math., 10, 205-208 (1970) · Zbl 0189.53104
[355] Vidossich, G., On a theorem of Corson and Lindenstrauss on Lindelöf function spaces, Israel J. Math., 9, 271-278 (1971) · Zbl 0192.59603
[356] Vidossich, G., On compactness in function spaces, (Proc. Amer. Math. Soc., 33 (1972)), 594-598 · Zbl 0216.40904
[357] Warner, S., The topology of compact convergence on continuous function spaces, Duke Math. J., 25, 2, 265-282 (1959) · Zbl 0081.32802
[358] de Wilde, M., Pointwise compactness in spaces of functions and R.C. James theorem, Math. Ann., 208, 33-47 (1974) · Zbl 0274.46019
[359] Yakovlev, N. N., On bicompacta in Σ-products and related spaces, Comment. Math. Univ. Carolin., 21, 2, 263-283 (1980) · Zbl 0436.54019
[360] I.V. Yaschenko, On monotonic normality of spaces of functions, Vestnik. Moskov. Univ. Ser. Mat. Mekh.; I.V. Yaschenko, On monotonic normality of spaces of functions, Vestnik. Moskov. Univ. Ser. Mat. Mekh.
[361] Yoshioka, I., Note on topologies for function spaces, Math. Japonica, 25, 373-377 (1980) · Zbl 0453.54008
[362] Young, N. J., Compactness in function spaces; another proof of a theorem of J.D. Pryce, J. London Math. Soc., 6, 739-740 (1973) · Zbl 0258.54013
[363] Zenor, P., Hereditary \(m\)-separability and hereditary \(m- Lindelöf\) property in product spaces and function spaces, Fund. Math., 106, 175-180 (1980) · Zbl 0454.54011
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