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On Katětov Spaces

Published online by Cambridge University Press:  20 November 2018

Jack Porter  and
Mohan Tikoo
Jack Porter
Affiliation:
Department of Mathematics University of Kansas Lawrence, KS 66045
Mohan Tikoo
Affiliation:
Department of Mathematics Southeast Missouri State University Cape Girardeau, MO 63701
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Abstract

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Recent work by Krystock, Porter, and Vermeer has emphasized the importance of the concepts of Katětov spaces and H-sets in the theory of H-closed spaces. These properties are closely related to being the θ-closure of some set and being the adherence of an open filter. This relationship is developed by establishing, among other facts, that an H-closed space in which every closed set is the θ-closure of some set is compact and the θ-closure of a subset of an H-closed space is Katětov and characterizing the open filter adhérences of a space as precisely those sets which are the image of a closed set of the absolute of the space. Also, examples are given of a countable, scattered space which is not Katětov and an H-closed space with an H-closed subspace which is not the θ-closure of any subset of the given space.

Keywords

54D2554C10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 32 , Issue 4 , 01 December 1989 , pp. 425 - 433
Copyright
Copyright © Canadian Mathematical Society 1989

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