A strengthening of the Katětov-Tong insertion theorem

Tomasz Kubiak

Commentationes Mathematicae Universitatis Carolinae (1993)

  • Volume: 34, Issue: 2, page 357-362
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Kubiak, Tomasz. "A strengthening of the Katětov-Tong insertion theorem." Commentationes Mathematicae Universitatis Carolinae 34.2 (1993): 357-362. <http://eudml.org/doc/247493>.

@article{Kubiak1993,
abstract = {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.},
author = {Kubiak, Tomasz},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {normal space; semicontinuous functions; insertion; limit functions; completely normal space; limit functions; insertion; Katětov-Tong theorem; semicontinuous functions; completely normal spaces},
language = {eng},
number = {2},
pages = {357-362},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A strengthening of the Katětov-Tong insertion theorem},
url = {http://eudml.org/doc/247493},
volume = {34},
year = {1993},
}

TY - JOUR
AU - Kubiak, Tomasz
TI - A strengthening of the Katětov-Tong insertion theorem
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1993
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 34
IS - 2
SP - 357
EP - 362
AB - 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.
LA - eng
KW - normal space; semicontinuous functions; insertion; limit functions; completely normal space; limit functions; insertion; Katětov-Tong theorem; semicontinuous functions; completely normal spaces
UR - http://eudml.org/doc/247493
ER -

References

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  13. Michael E., Continuous selections I, Annals of Math. 63 (1956), 361-382. (1956) Zbl0071.15902MR0077107
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  15. Priestley H.A., Separation theorems for semicontinuous functions on normally ordered topological spaces, J. London Math. Soc. (2) 3 (1971), 371-377. (1971) MR0278268
  16. Rodabaugh S.E., Höhle U., Klement E.P. (Eds.), Applications of Category Theory to Fuzzy Subsets, Kluwer Academic Publ., Dordrecht, 1992, p. 348. MR1154566
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  18. Tong H., Some characterizations of normal and perfectly normal spaces, Duke Math. J. 19 (1952), 289-292. (1952) Zbl0046.16203MR0050265

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