Preservation of completeness under mappings in asymmetric topology
Submitted: 2014-05-27
|Accepted: 2014-05-27
|Published: 2000-10-01
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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.
