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Proceedings of the American Mathematical Society

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



Decompositions of spaces determined by compact subsets

Author: Yoshio Tanaka
Journal: Proc. Amer. Math. Soc. 97 (1986), 549-555
MSC: Primary 54D50; Secondary 54E60
MathSciNet review: 840644
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Abstract: Let $ X$ be a $ k'$-space, and let $ \mathcal{F}$ be a closed cover of (locally) compact subsets of $ X$. Then $ X$ is decomposed into a closed discrete subset and a locally compact subset if $ X$ is dominated by $ \mathcal{F}$, or $ X$ has the weak topology with respect to a point-countable cover $ \mathcal{F}$. Here, a cover of a space is point-countable if every point is in at most countably many elements of the cover.

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Keywords: Weak topology, $ k$-space, $ k'$-space, locally compact space, quotient map, pseudo-open map, closed map
Article copyright: © Copyright 1986 American Mathematical Society