Spaces in which compact sets have countable local bases
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- by Ralph R. Sabella PDF
- Proc. Amer. Math. Soc. 48 (1975), 499-504 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
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Additional 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