Sandwich-type characterization of completely regular spaces
DOI:
https://doi.org/10.4995/agt.2007.1887Keywords:
Insertion, Sandwich theorem, Insertion theorem, Completely regular space, Lower semicontinuous, Upper semicontinuous, Compact.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.Downloads
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