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Keywords:
normal space; semicontinuous functions; insertion; limit functions; completely normal space
normal space; semicontinuous functions; insertion; limit functions; completely normal space
Summary:
Normal spaces are characterized in terms of an insertion type theorem, which implies the Katětov-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.
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