Continuously perfectly normal spaces and some generalizations
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- by Gary Gruenhage PDF
- Trans. Amer. Math. Soc. 224 (1976), 323-338 Request permission
Abstract:
In this work we continue the study of continuously perfectly normal, continuously normal, and continuously completely regular spaces which was begun by Phillip Zenor. Among other results, we prove that separable continuously completely regular spaces are metrizable, and provide an example of a nonmetrizable continuously perfectly normal space.References
- Carlos J. R. Borges, On stratifiable spaces, Pacific J. Math. 17 (1966), 1–16. MR 188982 —, Four generalizations of stratifiable spaces, Proc. Prague Topology Sympos., 1971 (to appear).
- Carlos J. R. Borges, On metrizability of topological spaces, Canadian J. Math. 20 (1968), 795–804. MR 231355, DOI 10.4153/CJM-1968-078-1
- Gary Gruenhage, Infinite games and generalizations of first-countable spaces, General Topology and Appl. 6 (1976), no. 3, 339–352. MR 413049
- John L. Kelley, General topology, D. Van Nostrand Co., Inc., Toronto-New York-London, 1955. MR 0070144
- K. Kuratowski, Topology. Vol. I, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe [Polish Scientific Publishers], Warsaw, 1966. New edition, revised and augmented; Translated from the French by J. Jaworowski. MR 0217751
- Louis F. McAuley, A relation between perfect separability, completeness, and normality in semi-metric spaces, Pacific J. Math. 6 (1956), 315–326. MR 80907
- Ernest Michael, Topologies on spaces of subsets, Trans. Amer. Math. Soc. 71 (1951), 152–182. MR 42109, DOI 10.1090/S0002-9947-1951-0042109-4
- E. A. Michael, A quintuple quotient quest, General Topology and Appl. 2 (1972), 91–138. MR 309045
- Jun-iti Nagata, On a necessary and sufficient condition of metrizability, J. Inst. Polytech. Osaka City Univ. Ser. A 1 (1950), 93–100. MR 43448 R. C. Olsen, Bi-quotient maps, countably bi-sequential spaces, and related problems, Doctoral Dissertation, University of Washington, Seattle, Washington.
- Frank Siwiec, Sequence-covering and countably bi-quotient mappings, General Topology and Appl. 1 (1971), no. 2, 143–154. MR 288737
- R. M. Stephenson Jr., Discrete subsets of perfectly normal spaces, Proc. Amer. Math. Soc. 34 (1972), 605–608. MR 296885, DOI 10.1090/S0002-9939-1972-0296885-5
- Hisahiro Tamano and J. E. Vaughan, Paracompactness and elastic spaces, Proc. Amer. Math. Soc. 28 (1971), 299–303. MR 273568, DOI 10.1090/S0002-9939-1971-0273568-8
- Phillip Zenor, A metrization theorem, Colloq. Math. 27 (1973), 241–243. MR 334156, DOI 10.4064/cm-27-2-241-243
- Phillip Zenor, Some continuous separation axioms, Fund. Math. 90 (1975/76), no. 2, 143–158. MR 394561, DOI 10.4064/fm-90-2-143-158
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 224 (1976), 323-338
- MSC: Primary 54D15; Secondary 54E35
- DOI: https://doi.org/10.1090/S0002-9947-1976-0428275-4
- MathSciNet review: 0428275