Decompositions of spaces determined by compact subsets
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- by Yoshio Tanaka PDF
- Proc. Amer. Math. Soc. 97 (1986), 549-555 Request permission
Abstract:
Let $X$ be a $kā$-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.References
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Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 97 (1986), 549-555
- MSC: Primary 54D50; Secondary 54E60
- DOI: https://doi.org/10.1090/S0002-9939-1986-0840644-9
- MathSciNet review: 840644