# A strengthening of the Katětov-Tong insertion theorem

Commentationes Mathematicae Universitatis Carolinae (1993)

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

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topKubiak, 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 -

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