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Rings of real-valued continuous functions. I. (English) Zbl 0032.28603


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[1] P. Alexandroff, Bikompakte Erweiterungen topologischer Räume, Rec. Math. [Mat. Sbornik] N.S. 5(47) (1939), 403 – 423 (Russian, with German summary). · JFM 65.0878.01
[2] P. S. Alexandroff and H. Hopf, Topologie I, Berlin, Springer, 1935. (Reprinted by Edwards Bros., Ann Arbor, Mich.) · JFM 61.0602.07
[3] P. S. Alexandroff and Paul Urysohn, Mémoire sur les espaces topologiques compacts, Verhandelingen der Koninklijke Akademie van Wetenschapen te Amsterdam, Afdeeling Natuurkunde, vol. 14, no. 1. · JFM 55.0960.02
[4] Emil Artin and Otto Schreier, Algebraische Konstruktion reeler Körper, Abh. Math. Sem. Hansischen Univ. vol. 5 (1926) pp. 83-115. · JFM 52.0120.05
[5] Reinhold Baer, Über nicht-Archimedisch geordnet Körper, Sitzungsberichte der Heidelberger Akademie der Wissenschaften, 8 Abh. (Mathematisch-Naturwissenschaftliche Klasse), 1927, pp. 3-13.
[6] N. Bourbaki, Éléments de mathématique. Part I. Les structures fondamentales de l’analyse. Livre III. Topologie générale. Chapitres I et II, Actual. Sci. Ind., no. 858, Hermann & Cie., Paris, 1940 (French). · Zbl 0030.24102
[7] Eduard Čech, On bicompact spaces, Ann. of Math. (2) 38 (1937), no. 4, 823 – 844. · Zbl 0017.42803
[8] -, Sur la dimension des espaces parfaitement normaux, Česká akademie véd a Umění v Praze, Bulletin International vol. 33 (1932) pp. 38-55.
[9] E. W. Chittenden, On general topology and the relation of the properties of the class of all continuous functions to the properties of space, Trans. Amer. Math. Soc. 31 (1929), no. 2, 290 – 321. · JFM 55.0959.02
[10] Samuel Eilenberg, Banach space methods in topology, Ann. of Math. (2) 43 (1942), 568 – 579. · Zbl 0061.39801
[11] I. Gelfand, Normierte Ringe, Rec. Math. [Mat. Sbornik] N. S. 9 (51) (1941), 3 – 24 (German, with Russian summary). · JFM 67.0406.02
[12] I. Gelfand and A. N. Kolmogoroff, On rings of continuous functions on topological spaces, C. R. (Doklady) Acad. Sci. URSS. vol. 22 (1939) pp. 11-15. · JFM 65.0500.03
[13] I. Gelfand and G. Šilov, Über verschiedene Methoden der Einführung der Topologie in die Menge der maximalen Ideale eines normierten Ringes, Rec. Math. [Mat. Sbornik] N. S. 9 (51) (1941), 25 – 39 (German, with Russian summary). · JFM 67.0407.01
[14] Edwin Hewitt, A problem of set-theoretic topology, Duke Math. J. 10 (1943), 309 – 333. · Zbl 0060.39407
[15] Edwin Hewitt, Certain generalizations of the Weierstrass approximation theorem, Duke Math. J. 14 (1947), 419 – 427. · Zbl 0029.30302
[16] Edwin Hewitt, On two problems of Urysohn, Ann. of Math. (2) 47 (1946), 503 – 509. · Zbl 0060.39511
[17] N. Jacobson, A topology for the set of primitive ideals in an arbitrary ring, Proc. Nat. Acad. Sci. U. S. A. 31 (1945), 333 – 338. · Zbl 0060.07402
[18] Shizuo Kakutani, Concrete representation of abstract (\?)-spaces. (A characterization of the space of continuous functions.), Ann. of Math. (2) 42 (1941), 994 – 1024. · Zbl 0060.26604
[19] Mark Krein and Selim Krein, Sur l’espace des fonctions continues définies sur un bicompact de Hausdorff et ses sousespaces semiordonnés, Rec. Math. [Mat. Sbornik] N.S. 13(55) (1943), 1 – 38 (French, with Russian summary). · Zbl 0060.26701
[20] S. Mazur, Sur les anneaux lineaires, C. R. Acad. Sci. Paris vol. 207 (1938) pp. 1025-1027. · Zbl 0020.20101
[21] E. H. Moore, On the foundations of the theory of linear integral equations, Bull. Amer. Math. Soc. 18 (1912), no. 7, 334 – 362. · JFM 43.0424.02
[22] Masahiro Nakamura and Shizuo Kakutani, Banach limits and the Čech compactification of a countable discrete set, Proc. Imp. Acad. Tokyo 19 (1943), 224 – 229. · Zbl 0063.05891
[23] Bedřich Pospíšil, Remark on bicompact spaces, Ann. of Math. (2) 38 (1937), no. 4, 845 – 846. · Zbl 0017.42901
[24] G. E. Shilov, Ideals and subrings of the ring of continuous functions, C. R. (Doklady) Acad. Sci. URSS. vol. 22 (1939) pp. 7-10. · Zbl 0021.41102
[25] Ernest Steinitz, Algebraische Theorie der Körper, J. Reine Angew, Math. vol. 137 (1910) pp. 167-309. · JFM 41.0445.03
[26] M. H. Stone, Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc. 41 (1937), no. 3, 375 – 481. · Zbl 0017.13502
[27] John W. Tukey, Convergence and Uniformity in Topology, Annals of Mathematics Studies, no. 2, Princeton University Press, Princeton, N. J., 1940. · Zbl 0025.09102
[28] A. Tychonoff, Über die topologische Erweiterung von Räumen, Math. Ann. 102 (1930), no. 1, 544 – 561 (German). · JFM 55.0963.01
[29] Paul Urysohn, Über die Mächtigkeit der zusammenhängenden Mengen, Math. Ann. 94 (1925), no. 1, 262 – 295 (German). · JFM 51.0452.05
[30] B. L. van der Waerden, Moderne Algebra, 2d. ed., Berlin, Springer, 1937. (Reprinted by Unger, New York, 1943.) · JFM 63.0082.06
[31] Henry Wallman, Lattices and topological spaces, Ann. of Math. (2) 39 (1938), no. 1, 112 – 126. · Zbl 0018.33202
[32] André Weil, Sur les espaces à structure uniforme et sur la topologie générale, Actualités Scientifiques et Industrielles, no. 551, Paris, Hermann, 1937. · JFM 63.0569.04
[33] L. Pontrjagin, Topological groups, Princeton University Press, 1939. · JFM 65.0872.02
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