Preservation of completeness under mappings in asymmetric topology
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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1. Unsymmetric T0-quasi-metrics
Hans-Peter A. Künzi, Mark Sioen, Filiz Yıldız
Topology and its Applications vol: 279 first page: 107249 year: 2020
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