Sandwich-type characterization of completely regular spaces

Javier Gutiérrez García

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.

Keywords

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

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References

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Universitat Politècnica de València

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