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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Separability and minimal weak base topologies


Authors: S. W. Davis and R. M. Stephenson
Journal: Proc. Amer. Math. Soc. 74 (1979), 371-378
MSC: Primary 54D25; Secondary 54E25, 54E30
MathSciNet review: 524320
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Abstract: In this note, we present filter characterizations of minimal weakly first countable, minimal $ \mathcal{F}$, minimal $ {\mathcal{F}_r}$, weakly first countable-closed, $ \mathcal{F}$-closed, and $ {\mathcal{F}_r}$-closed spaces. Our main result is a generalization of G. M. Reed's theorem that every Moore-closed space is separable.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0524320-4
PII: S 0002-9939(1979)0524320-4
Keywords: Weakly first countable, $ \mathcal{F}$-space, $ {\mathcal{F}_r}$-space, feebly compact, Baire space
Article copyright: © Copyright 1979 American Mathematical Society