Sandwich-type characterization of completely regular spaces

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.