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Pair-Countable, Closure-Preserving Covers of Compact Sets

Part of: Fairly general properties

Published online by Cambridge University Press:  09 April 2009

Henry Potoczny
Henry Potoczny
Affiliation:
Department of Mathematics and Computer Science U.S. Air Force Institute of Technology Wright-Patterson, Ohio 45433
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Abstract

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In this paper, we prove the following results: (1) if a topological space X has a pair-countable, closure-preserving cover of compact sets, then X is locally paracompact at each point of X and X has a dense open subspace which is locally σ-compact. In addition, if X is also collectionwise-T2, then X is paracompact. Locally paracompact is taken to mean that each point X has an open set with paracompact closure.

MSC classification

Secondary: 54D45: Local compactness, $sigma$-compactness
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 44 , Issue 1 , February 1988 , pp. 138 - 142
Copyright
Copyright © Australian Mathematical Society 1988

References

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