Spaces in which compact sets have countable local bases

Author:
Ralph R. Sabella

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

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Abstract: -spaces and coconvergent spaces are examples of spaces in which compact sets have countable local bases (-spaces). Among the results related to -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 -space is metrizable if there exists a stratification satisfying a nesting-like condition.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1975-0370522-6

Keywords:
Open neighborhood assignments,
-linked sequences,
coconvergent,
contraconvergent,
stratifiable spaces,
Nagata spaces

Article copyright:
© Copyright 1975
American Mathematical Society