Preservation of completeness under mappings in asymmetric topology | Zendy

Hans-Peter A. Künzi | Zendy

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Preservation 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

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