Monotone normality and extension of functions
Commentationes Mathematicae Universitatis Carolinae (1995)
- Volume: 36, Issue: 3, page 563-578
- ISSN: 0010-2628
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topStares, Ian. "Monotone normality and extension of functions." Commentationes Mathematicae Universitatis Carolinae 36.3 (1995): 563-578. <http://eudml.org/doc/247761>.
@article{Stares1995,
abstract = {We provide a characterisation of monotone normality with an analogue of the Tietze-Urysohn theorem for monotonically normal spaces as well as answer a question due to San-ou concerning the extension of Urysohn functions in monotonically normal spaces. We also extend a result of van Douwen, giving a characterisation of $K_0$-spaces in terms of semi-continuous functions, as well as answer another question of San-ou concerning semi-continuous Urysohn functions.},
author = {Stares, Ian},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {monotonically normal; extension of functions; Tietze; Urysohn; $K_1$; $K_0$; monotone normality; Tietze-Urysohn theorem; monotonically normal spaces},
language = {eng},
number = {3},
pages = {563-578},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Monotone normality and extension of functions},
url = {http://eudml.org/doc/247761},
volume = {36},
year = {1995},
}
TY - JOUR
AU - Stares, Ian
TI - Monotone normality and extension of functions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1995
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 36
IS - 3
SP - 563
EP - 578
AB - We provide a characterisation of monotone normality with an analogue of the Tietze-Urysohn theorem for monotonically normal spaces as well as answer a question due to San-ou concerning the extension of Urysohn functions in monotonically normal spaces. We also extend a result of van Douwen, giving a characterisation of $K_0$-spaces in terms of semi-continuous functions, as well as answer another question of San-ou concerning semi-continuous Urysohn functions.
LA - eng
KW - monotonically normal; extension of functions; Tietze; Urysohn; $K_1$; $K_0$; monotone normality; Tietze-Urysohn theorem; monotonically normal spaces
UR - http://eudml.org/doc/247761
ER -
References
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- Scott B.M., A ``more topological'' proof of the Tietze-Urysohn theorem, Amer. Math. Monthly 85 (1978), 192-193. (1978) Zbl0376.54006MR0474185
- Stares I.S., Extension of functions and generalised metric spaces, D. Phil. Thesis, Oxford University, June 1994.
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