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An Ultrafilter Completion of a Nearness Space

Published online by Cambridge University Press:  20 November 2018

John W. Carlson
John W. Carlson*
Affiliation:
Mathematics Department, Emporia State University, Emporia, Kansas 66801, U.S.A.
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Abstract

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An ultrafilter completion is constructed for a nearness space. It is shown to preserve the Tl separation axiom. Characterizing conditions are given for it to be topological or for its topology to be compact. It is shown to have the simple extension topology and for a given Hausdorff space a compatible nearness structure is found for which its ultrafilter completion is homeomorphic to the Katetov H-closed extension.

Keywords

54-0254A0554B9954D9954E05Nearness spaceUltrafilter CompleteReflective SubcategoryH-closed
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 24 , Issue 1 , 01 March 1981 , pp. 13 - 22
Copyright
Copyright © Canadian Mathematical Society 1981

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