A note concerning completely regular $G_{\delta }$-spaces
HTML articles powered by AMS MathViewer
- by L. J. Heider PDF
- Proc. Amer. Math. Soc. 8 (1957), 1060-1066 Request permission
References
- Frank W. Anderson, A lattice characterization of completely regular $G_\delta$-spaces, Proc. Amer. Math. Soc. 6 (1955), 757–765. MR 72451, DOI 10.1090/S0002-9939-1955-0072451-1 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.
- 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. 5 (1954), 447–455. MR 66627, DOI 10.1090/S0002-9939-1954-0066627-6
- L. J. Heider, Directed limits on rings of continuous functions, Duke Math. J. 23 (1956), 293–296. MR 77106, DOI 10.1215/S0012-7094-56-02327-4
- Melvin Henriksen, On the equivalence of the ring, lattice, and semigroup of continuous functions, Proc. Amer. Math. Soc. 7 (1956), 959–960. MR 82490, DOI 10.1090/S0002-9939-1956-0082490-3
- Edwin Hewitt, Rings of real-valued continuous functions. I, Trans. Amer. Math. Soc. 64 (1948), 45–99. MR 26239, DOI 10.1090/S0002-9947-1948-0026239-9
- Irving Kaplansky, Lattices of continuous functions, Bull. Amer. Math. Soc. 53 (1947), 617–623. MR 20715, DOI 10.1090/S0002-9904-1947-08856-X
- A. N. Milgram, Multiplicative semigroups of continuous functions, Duke Math. J. 16 (1949), 377–383. MR 29476, DOI 10.1215/S0012-7094-49-01638-5
- R. S. Pierce, Coverings of a topological space, Trans. Amer. Math. Soc. 77 (1954), 281–298. MR 70149, DOI 10.1090/S0002-9947-1954-0070149-0
- Lyle E. Pursell, An algebraic characterization of fixed ideals in certain function rings, Pacific J. Math. 5 (1955), 963–969. MR 83478, DOI 10.2140/pjm.1955.5.963
- Taira Shirota, A generalization of a theorem of I. Kaplansky, Osaka Math. J. 4 (1952), 121–132. MR 52760
- 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
Additional Information
- © Copyright 1957 American Mathematical Society
- 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