Spaces in which compact sets have countable local bases
HTML articles powered by AMS MathViewer
- by Ralph R. Sabella
- Proc. Amer. Math. Soc. 48 (1975), 499-504
- DOI: https://doi.org/10.1090/S0002-9939-1975-0370522-6
- PDF | Request permission
Abstract:
${D_1}$-spaces and coconvergent spaces are examples of spaces in which compact sets have countable local bases (${D_0}$-spaces). Among the results related to ${D_0}$-spaces given in this paper is a sufficient condition under which such spaces are coconvergent. In relation to a question posed by F. B. Jones, it is shown that a topological property sufficient for semimetrizable spaces to be developable is that they be coconvergent. Coconvergence implies metrizability in stratifiable spaces; it is shown in this paper that a ${D_0}$-space is metrizable if there exists a stratification satisfying a nesting-like condition.References
- C. E. Aull, Closed set countability axioms, Indag. Math. 28 (1966), 311–316. Nederl. Akad. Wetensch. Proc. Ser. A 69. MR 0199833
- Carlos J. R. Borges, On stratifiable spaces, Pacific J. Math. 17 (1966), 1–16. MR 188982
- Jack G. Ceder, Some generalizations of metric spaces, Pacific J. Math. 11 (1961), 105–125. MR 131860
- Geoffrey D. Creede, Concerning semi-stratifiable spaces, Pacific J. Math. 32 (1970), 47–54. MR 254799 R. W. Heath, On certain first-countable spaces, Ann. of Math. Studies, no. 60, Princeton Univ. Press, Princeton, N.J., 1965, pp. 103-113.
- Ralph R. Sabella, Convergence properties of neighboring sequences, Proc. Amer. Math. Soc. 38 (1973), 405–409. MR 312479, DOI 10.1090/S0002-9939-1973-0312479-8 —, Properties of neighboring sequences in stratifiable spaces, Proc. Amer. Math. Soc. (submitted).
Bibliographic Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 48 (1975), 499-504
- MSC: Primary 54E35
- DOI: https://doi.org/10.1090/S0002-9939-1975-0370522-6
- MathSciNet review: 0370522