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...

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Detalles Bibliográficos
Autores: Gutiérrez García, Javier, Kubiak, Tomasz
Tipo de recurso: artículo
Fecha de publicación:2007
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:10251/83070
Acceso en línea:https://riunet.upv.es/handle/10251/83070
Access Level:acceso abierto
Palabra clave:Insertion
Sandwich theorem
Insertion theorem
Completely regular space
Lower semicontinuous
Upper semicontinuous
Compact
Descripción
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.