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...
| Authors: | ; |
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| Format: | Article |
| Publication date: | 2007 |
| Country: | España |
| Institution: | Universitat Politècnica de València (UPV) |
| Repository: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Language: | English |
| OAI Identifier: | oai:riunet.upv.es:10251/83070 |
| Online Access: | https://riunet.upv.es/handle/10251/83070 |
| Access Level: | Open access |
| Keyword: | Insertion Sandwich theorem Insertion theorem Completely regular space Lower semicontinuous Upper semicontinuous Compact |
| Summary: | [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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