Abstract:Normal spaces are characterized in terms of an insertion type theorem, which implies the Kat\v etov-Tong theorem. The proof actually provides a simple necessary and sufficient condition for the insertion of an ordered pair of lower and upper semicontinuous functions between two comparable real-valued functions. As a consequence of the latter, we obtain a characterization of completely normal spaces by real-valued functions.
Keywords: normal space, semicontinuous functions, insertion, limit functions, completely normal space
AMS Subject Classification: 54D15, 54C30