Geodesic
A strengthening of the Katětov-Tong insertion theorem
Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) no. 2, pp. 357-362

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MR Zbl
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.
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.
Classification : 54C30, 54D15
Keywords: normal space; semicontinuous functions; insertion; limit functions; completely normal space 
Kubiak, Tomasz. A strengthening of the Katětov-Tong insertion theorem. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) no. 2, pp. 357-362. http://geodesic.mathdoc.fr/item/CMUC_1993_34_2_a17/
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     title = {A strengthening of the {Kat\v{e}tov-Tong} insertion theorem},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {357--362},
     year = {1993},
     volume = {34},
     number = {2},
     mrnumber = {1241744},
     zbl = {0807.54023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1993_34_2_a17/}
}
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