Preservation of completeness under mappings in asymmetric topology

• Künzi, Hans-Peter A. ^[1]
  1. [1] University of Cape Town

     University of Cape Town

     City of Cape Town, Sudáfrica

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 1, Nº. 1, 2000, págs. 99-114
• Idioma: inglés
• DOI: 10.4995/agt.2000.3027
• Enlaces
  • Texto completo
• Resumen

  • 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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