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Completion of continuity spaces with uniformly vanishing asymmetry

Chand, Alveen and Weiss, Ittay (2015) Completion of continuity spaces with uniformly vanishing asymmetry. Topology and Its Applications, 183 . pp. 130-140. ISSN 0166-8641

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Abstract

The classical Cauchy completion of a metric space (by means of Cauchy sequences) as well as the completion of a uniform space (by means of Cauchy filters) are well-known to rely on the symmetry of the metric space or uniform space in question. For qausi-metric spaces and quasi-uniform spaces various non-equivalent completions exist, often defined on a certain subcategory of spaces that satisfy a key property required for the particular completion to exist. The classical filter completion of a uniform space can be adapted to yield a filter completion of a metric space. We show that this completion by filters generalizes to continuity spaces that satisfy a form of symmetry which we call uniformly vanishing asymmetry.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Technology and Environment (FSTE) > School of Computing, Information and Mathematical Sciences
Depositing User: Ittay Weiss
Date Deposited: 01 Oct 2015 17:18
Last Modified: 14 Sep 2016 09:59
URI: http://repository.usp.ac.fj/id/eprint/8442
UNSPECIFIED

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