Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54D50, 54E60

Retrieve articles in all journals with MSC: 54D50, 54E60


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1986-0840644-9
Keywords: Weak topology, $ k$-space, $ k'$-space, locally compact space, quotient map, pseudo-open map, closed map
Article copyright: © Copyright 1986 American Mathematical Society