Preservation of completeness under mappings in asymmetric topology
[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 preserve...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2000 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/81899 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/81899 |
| Access Level: | acceso abierto |
| Palabra clave: | Uniformly open mapping Almost uniformly open mapping Open mapping theorem Quasi-metrizable Left K-complete Open mapping Closed mapping Supercomplete Aronszajn space |
| Sumario: | [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. |
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