Preservation of completeness under mappings in asymmetric topology

Authors

  • Hans-Peter A. Künzi University of Cape Town

DOI:

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

Keywords:

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

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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Author Biography

Hans-Peter A. Künzi, University of Cape Town

Department of Mathematics and Applied Mathematics

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Published

2000-10-01

How to Cite

[1]
H.-P. A. Künzi, “Preservation of completeness under mappings in asymmetric topology”, Appl. Gen. Topol., vol. 1, no. 1, pp. 99–114, Oct. 2000.

Issue

Section

Regular Articles