1. Preservation of completeness under mappings in asymmetric topology
- Author
-
Hans-Peter A. Künzi
- Subjects
Discrete mathematics ,Almost uniformly open mapping ,Moore space (topology) ,Left K-complete ,Open mapping ,lcsh:Mathematics ,Open mapping theorem ,Open set ,lcsh:QA299.6-433 ,Uniformly open mapping ,lcsh:Analysis ,Topology ,Space (mathematics) ,lcsh:QA1-939 ,Aronszajn space ,Open and closed maps ,Closed mapping ,Completeness (order theory) ,Geometry and Topology ,Open mapping theorem (functional analysis) ,Filter (mathematics) ,Quasi-metrizable ,Supercomplete ,Bijection, injection and surjection ,Mathematics - Abstract
[EN] 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., This paper was written while the author was supported by the Swiss National Science Foundation under grant 2000-056811.99. He also acknowledges support during a visit to the University of Oxford by the Stiftung zur F orderung der wissenschaftlichen Forschung an der Universit at Bern.
- Published
- 2000