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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
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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