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A strengthening of the Katětov-Tong insertion theorem. (English) Zbl 0807.54023
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.

MSC:
54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)
54C30 Real-valued functions in general topology
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