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Transactions of the American Mathematical Society

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Concerning rings of continuous functions


Authors: Leonard Gillman and Melvin Henriksen
Journal: Trans. Amer. Math. Soc. 77 (1954), 340-362
MSC: Primary 56.0X
DOI: https://doi.org/10.1090/S0002-9947-1954-0063646-5
MathSciNet review: 0063646
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  • [1] R. Arens and I. Kaplansky, Topological representations of algebras, Trans. Amer. Math. Soc. vol. 63 (1948) pp. 457-481. MR 0025453 (10:7c)
  • [2] E. Čech, On bicompact spaces, Ann. of Math. vol. 38 (1937) pp. 823-844. MR 1503374
  • [3] J. Dieudonné, Une généralisation des espaces compacts, J. Math. Pures Appl. vol. 23 (1944) pp. 65-76. MR 0013297 (7:134f)
  • [4] C. H. Dowker, On countably compact spaces, Canadian Journal of Mathematics vol. 3 (1951) pp. 219-224. MR 0043446 (13:264c)
  • [5] L. Gillman, M. Henriksen, and M. Jerison, On a theorem of Gelfand and Kolmogoroff concerning maximal ideals in rings of continuous functions, Proc. Amer. Math. Soc. vol. 5 (1954) pp. 447-455. MR 0066627 (16:607h)
  • [6] F. Hausdorff, Grundzüge einer Theorie der geordneten Mengen, Math. Ann. vol. 65 (1908) pp. 435-505. MR 1511478
  • [7] -, Grundzüge der Mengenlehre, Leipzig, 1914.
  • [8] M. Henriksen, On the prime ideals of the ring of entire functions, Pacific Journal of Mathematics vol. 3 (1953) pp. 711-720. MR 0059479 (15:537c)
  • [9] M. Henriksen and J. R. Isbell, On the continuity of the real roots of an algebraic equation, Proc. Amer. Math. Soc. vol. 4 (1953) pp. 431-434. MR 0055664 (14:1107e)
  • [10] E. Hewitt, Rings of real-valued continuous functions, I, Trans. Amer. Math. Soc. vol. 64 (1948) pp. 45-99. MR 0026239 (10:126e)
  • [11] -, Linear functionals on spaces of continuous functions, Fund. Math. vol. 37 (1950) pp. 161-189. MR 0042684 (13:147g)
  • [12] I. Kaplansky, Topological rings, Amer. J. Math. vol. 69 (1947) pp. 153-183. MR 0019596 (8:434b)
  • [13] M. Katětov, Measures in fully normal spaces, Fund Math. vol. 38 (1951) pp. 73-84. MR 0048531 (14:27c)
  • [14] C. Kuratowski, Topologie I, Warsaw, 1933.
  • [15] S. Lefschetz, Algebraic topology, Amer. Math. Soc. Colloquium Publications, vol. 27, 1942.
  • [16] N. H. McCoy, Rings and ideals, Mathematical Association of America, 1948. MR 0026038 (10:96b)
  • [17] B. Pospíšil, Remark on bicompact spaces, Ann. of Math. vol. 38 (1937) pp. 845-846. MR 1503375
  • [18] T. Shirota, A class of topological spaces, Osaka Math. J. vol. 4 (1952) pp. 23-40. MR 0050872 (14:395b)
  • [19] R. Sikorski, Remarks on some topological spaces of high power, Fund. Math. vol. 37 (1950) pp. 125-136. MR 0040643 (12:727e)
  • [20] A. H. Stone, Paracompactness and product spaces, Bull. Amer. Math. Soc. vol. 54 (1948) pp. 977-982. MR 0026802 (10:204c)
  • [21] M. H. Stone, Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc. vol. 41 (1937) pp. 375-481. MR 1501905
  • [22] A. Tarski, Über unerreichbare Kardinalzahlen, Fund. Math. vol. 30 (1938) pp. 68-89.
  • [23] -, Drei Überdeckungssätze der allgemeinen Mengenlehre, Fund. Math. vol. 30 (1938) pp. 132-155.
  • [24] A. Tychonoff, Über die topologische Erweiterung von Räumen, Math. Ann. vol. 102 (1930) pp. 544-561. MR 1512595
  • [25] S. Ulam, Zur Masstheorie in der allgemeinen Mengenlehre, Fund. Math. vol. 16 (1930) pp. 140-150.
  • [26] B. L. van der Waerden, Moderne Algebra, Berlin, 1940.

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DOI: https://doi.org/10.1090/S0002-9947-1954-0063646-5
Article copyright: © Copyright 1954 American Mathematical Society

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