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Closure-preserving families of compact sets

✍ Scribed by H.B. Potoczny

Publisher: Elsevier Science
Year: 1973
Weight: 750 KB
Volume: 3
Category: Article
ISSN: 0016-660X
DOI: 10.1016/0016-660x(72)90015-3

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✦ Synopsis

In [ 31, Tamano raised the question of whether or not a space which admits a closurepreserving cova'r of compact sets is nzce:ssari!y paracon+:t.

b cn~~etexamplc to this oonjectuse was given in 161: a completely rqular 1'2 space having a t losIre-preserving cover by compact sets (in fact, by finite sets) which 'Cails to be paracompact or even normal. It is the purpf3se of this paper to show that if X is a a.;lle:ctionwi~norma! T1 space which admits such a cover, then X is pwacompact.

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