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Bicompleteness of the fine quasi-uniformity

Published online by Cambridge University Press:  24 October 2008

Hans-Peter A. Künzi  and
Nathalie Ferrario
Hans-Peter A. Künzi
Affiliation:
Department of Mathematics, University of Berne, Sidlerstrasse 5, 3012 Berne, Switzerland
Nathalie Ferrario
Affiliation:
Department of Mathematics, University of Berne, Sidlerstrasse 5, 3012 Berne, Switzerland
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Abstract

A characterization of the topological spaces that possess a bicomplete fine quasi-uniformity is obtained. In particular we show that the fine quasi-uniformity of each sober space, of each first-countable T1-space and of each quasi-pseudo-metrizable space is bicomplete. Moreover we give examples of T1-spaces that do not admit a bicomplete quasi-uniformity.

We obtain several conditions under which the semi-continuous quasi-uniformity of a topological space is bicomplete and observe that the well-monotone covering quasiuniformity of a topological space is bicomplete if and only if the space is quasi-sober.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 109 , Issue 1 , January 1991 , pp. 167 - 186
Copyright
Copyright © Cambridge Philosophical Society 1991

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