Open AccessPreservation of completeness under mappings in asymmetric topology
Author(s) -
Hans-Peter A. Künzi
Publication year - 2000
Publication title -
applied general topology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.638
H-Index - 13
eISSN - 1989-4147
pISSN - 1576-9402
DOI - 10.4995/agt.2000.3027
Subject(s) - mathematics , metrization theorem , metric space , uniform continuity , completeness (order theory) , topological space , pure mathematics , t1 space , topology (electrical circuits) , discrete mathematics , isolated point , combinatorics , mathematical analysis , topological vector space , separable space
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