Sandwich-type characterization of completely regular spaces
[EN] All the higher separation axioms in topology, except for complete regularity, are known to have sandwich-type characterizations. This note provides a characterization of complete regularity in terms of inserting a continuous real-valued function. The known fact that each continuous real valued...
| Autores: | ; |
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| Tipo de documento: | Artículo |
| Fecha de publicación: | 2007 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Lenguaje: | Inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/83070 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/83070 |
| Nivel de acceso: | Acceso abierto |
| Palabra clave: | Insertion Sandwich theorem Insertion theorem Completely regular space Lower semicontinuous Upper semicontinuous Compact |
| Sumario: | [EN] All the higher separation axioms in topology, except for complete regularity, are known to have sandwich-type characterizations. This note provides a characterization of complete regularity in terms of inserting a continuous real-valued function. The known fact that each continuous real valued function on a compact subset o fa Tychonoff space has a continuous extension to the whole space is obtained as a corollary. |
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