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Absolutes of almost realcompactifications

Part of: Fairly general properties

Published online by Cambridge University Press:  09 April 2009

Mohan L. Tikoo
Mohan L. Tikoo
Affiliation:
Department of Mathematics, Southeast Missouri State University, Cape Girardeau, Missouri 63701, U.S.A.
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Abstract

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Given Hausdorff spaces X and Y and a perfect irreducible and θ-continuous map f from X onto Y, technique that carries open (ultra) filters on X to open (ultra) filters on Y back and forth in a natural way is introduced. It is proved that if f is a perfect irreducible and θ-continuous map from X onto Y, then X is almost realcompact if and only if Y is almost realcompact. Several commutativity relations between the ‘absolutes of almost realcompactifications’ and the ‘almost realcompactifications of absólutes’ of a space X are discussed.

Keywords

absolutesH-closed spacesalmost realcompact spaces

MSC classification

Secondary: 54D25: “$P$-minimal” and “$P$-closed” spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 41 , Issue 2 , October 1986 , pp. 251 - 267
Copyright
Copyright © Australian Mathematical Society 1986

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