A curious example involving ordered compactifications
[EN] For a certain product X x Y where X is compact, connected, totally ordered space, we find that the semilattice K0 (X x Y) of ordered compactifications of X x Y is isomorphic to a collection of Galois connections and to a collection of functions F which determines a quasi-uniformity on an extend...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2002 |
| 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:10251/82059 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/82059 |
| Access Level: | acceso abierto |
| Palabra clave: | Ordered topological space Ordered compactification Galois connection Quasi-uniformity F-poset |
| Sumario: | [EN] For a certain product X x Y where X is compact, connected, totally ordered space, we find that the semilattice K0 (X x Y) of ordered compactifications of X x Y is isomorphic to a collection of Galois connections and to a collection of functions F which determines a quasi-uniformity on an extended set X U {+∞}, from which the topology and order on X is easily recovered. It is well-known that each ordered compactification of an ordered space X x Y corresponds to a totally bounded quasi-uniformity on X x Y compatible with the topology and order on X x Y, and thus K0 (X x Y) may be viewed as a collection of quasi-uniformities on X x Y. By the results here, these quasi-uniformities on X x Y determine a quasi-uniformity on the related space X U {+∞}. |
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