Preservation of completeness under mappings in asymmetric topology

Hans-Peter A. Künzi

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.


Keywords

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

Subject classification

54C10; 54E15; 54E35;54E50

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1. Unsymmetric T0-quasi-metrics
Hans-Peter A. Künzi, Mark Sioen, Filiz Yıldız
Topology and its Applications  vol: 279  first page: 107249  year: 2020  
doi: 10.1016/j.topol.2020.107249



Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt