Monotone normality and extension of functions
Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 3, pp. 563-578
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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.
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.
Classification :
54C20, 54D15, 54E50
Keywords: monotonically normal; extension of functions; Tietze; Urysohn; $K_1$; $K_0$
Keywords: monotonically normal; extension of functions; Tietze; Urysohn; $K_1$; $K_0$
@article{CMUC_1995_36_3_a17,
author = {Stares, I. S.},
title = {Monotone normality and extension of functions},
journal = {Commentationes Mathematicae Universitatis Carolinae},
pages = {563--578},
year = {1995},
volume = {36},
number = {3},
mrnumber = {1364497},
zbl = {0882.54012},
language = {en},
url = {http://geodesic.mathdoc.fr/item/CMUC_1995_36_3_a17/}
}
Stares, I. S. Monotone normality and extension of functions. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 3, pp. 563-578. http://geodesic.mathdoc.fr/item/CMUC_1995_36_3_a17/