Sandwich-type characterization of completely regular spaces

Javier Gutiérrez García

Spain

Universidad del País Vasco

Departamento de Matemáticas

Submitted: 2013-11-15

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Accepted: 2013-11-15

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DOI: https://doi.org/10.4995/agt.2007.1887
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Keywords:

Insertion, Sandwich theorem, Insertion theorem, Completely regular space, Lower semicontinuous, Upper semicontinuous, Compact.

Supporting agencies:

Ministry of Education and Science of Spain and FEDER under grant MTM2006-14925-C02-02. University of the Basque Country under grant UPV05/101.

Abstract:

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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