Characterization of the space of continuous functions over a compact Hausdorff space
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- by R. F. Arens and J. L. Kelley PDF
- Trans. Amer. Math. Soc. 62 (1947), 499-508 Request permission
References
- Leon Alaoglu, Weak topologies of normed linear spaces, Ann. of Math. (2) 41 (1940), 252–267. MR 1455, DOI 10.2307/1968829 S. Banach, Théorie des opérations linéaires, Warsaw, 1932.
- H. F. Bohnenblust and S. Kakutani, Concrete representation of $(M)$-spaces, Ann. of Math. (2) 42 (1941), 1025–1028. MR 5779, DOI 10.2307/1968779
- Samuel Eilenberg, Banach space methods in topology, Ann. of Math. (2) 43 (1942), 568–579. MR 7974, DOI 10.2307/1968812 I. Gelfand, On normed rings, C. R. (Doklady) Acad. Sci. URSS. vol. 23 (1939) pp. 430-432.
- Shizuo Kakutani, Concrete representation of abstract $(M)$-spaces. (A characterization of the space of continuous functions.), Ann. of Math. (2) 42 (1941), 994–1024. MR 5778, DOI 10.2307/1968778
- Mark Krein and Selim Krein, On an inner characteristic of the set of all continuous functions defined on a bicompact Hausdorff space, C. R. (Doklady) Acad. Sci. URSS (N.S.) 27 (1940), 427–430. MR 0003453
- M. Krein and D. Milman, On extreme points of regular convex sets, Studia Math. 9 (1940), 133–138 (English, with Ukrainian summary). MR 4990, DOI 10.4064/sm-9-1-133-138 S. Saks, Theory of the integral, Warsaw-Lwów, 1937.
- S. Saks, Integration in abstract metric spaces, Duke Math. J. 4 (1938), no. 2, 408–411. MR 1546062, DOI 10.1215/S0012-7094-38-00433-8
- M. H. Stone, Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc. 41 (1937), no. 3, 375–481. MR 1501905, DOI 10.1090/S0002-9947-1937-1501905-7
- M. H. Stone, A general theory of spectra. I, Proc. Nat. Acad. Sci. U.S.A. 26 (1940), 280–283. MR 2023, DOI 10.1073/pnas.26.4.280
- M. H. Stone, A general theory of spectra. II, Proc. Nat. Acad. Sci. U.S.A. 27 (1941), 83–87. MR 4092, DOI 10.1073/pnas.27.1.83
Additional Information
- © Copyright 1947 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 62 (1947), 499-508
- MSC: Primary 46.0X
- DOI: https://doi.org/10.1090/S0002-9947-1947-0022999-0
- MathSciNet review: 0022999