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On coabsolute paracompact spaces

Part of: Peculiar spaces Fairly general properties

Published online by Cambridge University Press:  09 April 2009

Catherine L. Gates
Catherine L. Gates
Affiliation:
Franklin and Marshall College Lancaster, Pennsylvania 17604, U.S.A.
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Abstract

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We are interested in determining whether two spaces are coabsolute by comparing their Boolean algebras of regular closed sets. It is known that when the spaces are compact Hausdorff they are coabsolute precisely when the Boolean algebras of regular closed sets are isomorphic; but in general this condition is not strong enough to insure that the spaces be coabsolute. In this paper we show that for paracompact Hausdorff spaces, the spaces are coabsolute when the Boolean algebra isomorphism and its inverse ‘preserve’ local finiteness, and for locally compact paracompact Hausdorff spaces, the spaces are coabsolute when the collections of compact regular closed subsets are ‘isomorphic’.

Keywords

coabsolute spacesBoolean algebra of regular closed sets.

MSC classification

Secondary: 54D20: Noncompact covering properties (paracompact, Lindelöf, etc.) 54D45: Local compactness, $sigma$-compactness 54G05: Extremally disconnected spaces, $F$-spaces, etc.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 27 , Issue 2 , March 1979 , pp. 248 - 256
Copyright
Copyright © Australian Mathematical Society 1979

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