J Austral Math Soc Ser A 44 pp138--142, 1988.

Pair-Countable, CLosure-Preserving Covers of Compact Sets

Henry Potoczny

(Received 29 November 1983; revised 26 February 1986)

Abstract

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 paircompact at each point of X and X has a dense open subspace which is locally s-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.

1980 AMS Subject Classification: primary 54D18; secondary 54D45

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Authors

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

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Last Modified: Wed Feb 19 10:27:48 2003