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A note concerning completely regular $ G\sb{\delta }$-spaces


Author: L. J. Heider
Journal: Proc. Amer. Math. Soc. 8 (1957), 1060-1066
MSC: Primary 54.00; Secondary 46.00
DOI: https://doi.org/10.1090/S0002-9939-1957-0096194-5
MathSciNet review: 0096194
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  • [1] F. W. Anderson, A lattice characterization of completely regular $ {G_\delta }$ spaces, Proc. Amer. Math. Soc. vol. 6 (1955) pp. 757-765. MR 0072451 (17:287a)
  • [2] 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.
  • [3] 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)
  • [4] L. J. Heider, Directed limits on rings of continuous functions, Duke Math. J. vol. 23 (1956) pp. 293-296. MR 0077106 (17:990d)
  • [5] M. Henriksen, On the equivalence of the ring, lattice and semigroup of continuous functions, Proc. Amer. Math. Soc. vol. 7 (1956) pp. 959-960. MR 0082490 (18:559a)
  • [6] E. Hewitt, Rings of real-valued continuous functions. I, Trans. Amer. Math. Soc. vol. 64 (1948) pp. 45-99. MR 0026239 (10:126e)
  • [7] I. Kaplansky, Lattices of continuous functions, Bull. Amer. Math. Soc. vol 53 (1947) pp. 617-623. MR 0020715 (8:587e)
  • [8] A. N. Milgram, Multiplicative semigroups of continuous functions, Duke Math. J. vol. 16 (1949) pp. 377-383. MR 0029476 (10:612a)
  • [9] R. Pierce, Coverings of a topological space, Trans. Amer. Math. Soc. vol. 77 (1954) pp. 281-289. MR 0070149 (16:1138e)
  • [10] L. E. Pursell, An algebraic characterization of fixed ideals in certain function rings, Pacific J. Math. Supplement II (1955) pp. 963-971. MR 0083478 (18:714e)
  • [11] T. Shirota, A generalization of a theorem of I. Kaplansky, Osaka Mathematical Journal vol. 4 (1952) pp. 121-132. MR 0052760 (14:669b)
  • [12] M. H. Stone, Applications of the theory of Boolean rings in general topology, Trans. Amer. Math. Soc. vol. 41 (1937) pp. 375-481. MR 1501905

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DOI: https://doi.org/10.1090/S0002-9939-1957-0096194-5
Article copyright: © Copyright 1957 American Mathematical Society

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