Decompositions of spaces determined by compact subsets

Author:
Yoshio Tanaka

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

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Abstract: Let be a -space, and let be a closed cover of (locally) compact subsets of . Then is decomposed into a closed discrete subset and a locally compact subset if is dominated by , or has the weak topology with respect to a point-countable cover . 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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1986-0840644-9

Keywords:
Weak topology,
-space,
-space,
locally compact space,
quotient map,
pseudo-open map,
closed map

Article copyright:
© Copyright 1986
American Mathematical Society