Preservation of completeness under mappings in asymmetric topology

Hans-Peter A. Künzi

South Africa

University of Cape Town

Department of Mathematics and Applied Mathematics
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Accepted: 2014-05-27

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Published: 2000-10-01

DOI: https://doi.org/10.4995/agt.2000.3027
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Keywords:

Uniformly open mapping, Almost uniformly open mapping, Open mapping theorem, Quasi-metrizable, Left K-complete, Open mapping, Closed mapping, Supercomplete, Aronszajn space

Supporting agencies:

Swiss National Science Foundation (under grant 2000-056811.99)

Abstract:

The preservation of various completeness properties in the quasi-metric (and quasi-uniform) setting under open, closed and uniformly open mappings is investigated. In particular, it is noted that between quasi-uniform spaces the property that each costable filter has a cluster point is preserved under uniformly open continuous surjections.  Furthermore in the realm of quasi-uniform spaces conditions under which almost uniformly open mappings are uniformly open are given which generalize corresponding classical results for uniform spaces. As a by-product it is shown that a quasi-metrizable Moore space admits a left K-complete quasi-metric if and only if it is a complete Aronszajn space.

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