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: | ; |
|---|---|
| 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 |
| _version_ | 1878736734123982848 |
|---|---|
| author | Gutiérrez García, Javier |
| author2 | Kubiak, Tomasz |
| author2_role | author |
| author_browse | Gutiérrez García, Javier Kubiak, Tomasz |
| author_facet | Gutiérrez García, Javier Kubiak, Tomasz |
| author_role | author |
| collection | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| description | [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. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | ES_9457fd79110f14452ab3a32f9e7a5b05 |
| institution | Universitat Politècnica de València (UPV) |
| instname_str | Universitat Politècnica de València (UPV) |
| language | eng |
| network_acronym_str | ES |
| network_name_str | España |
| oai_identifier_str | oai:riunet.upv.es:10251/83070 |
| publishDate | 2007 |
| publishDateSort | 2007 |
| publisher | Universitat Politècnica de València |
| publisherStr | Universitat Politècnica de València |
| reponame_str | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| spelling | Sandwich-type characterization of completely regular spaces Gutiérrez García, Javier Kubiak, Tomasz Insertion Sandwich theorem Insertion theorem Completely regular space Lower semicontinuous Upper semicontinuous Compact [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. This research was supported by the Ministry of Education and Science of Spain and FEDER under grant MTM2006-14925-C02-02. Universitat Politècnica de València https://riunet.upv.es/handle/10251/83070 |
| spellingShingle | Sandwich-type characterization of completely regular spaces Gutiérrez García, Javier Insertion Sandwich theorem Insertion theorem Completely regular space Lower semicontinuous Upper semicontinuous Compact |
| title | Sandwich-type characterization of completely regular spaces |
| title_full | Sandwich-type characterization of completely regular spaces |
| title_fullStr | Sandwich-type characterization of completely regular spaces |
| title_full_unstemmed | Sandwich-type characterization of completely regular spaces |
| title_short | Sandwich-type characterization of completely regular spaces |
| title_sort | Sandwich-type characterization of completely regular spaces |
| topic | Insertion Sandwich theorem Insertion theorem Completely regular space Lower semicontinuous Upper semicontinuous Compact |
| topic_facet | Insertion Sandwich theorem Insertion theorem Completely regular space Lower semicontinuous Upper semicontinuous Compact |
| url | https://riunet.upv.es/handle/10251/83070 |