Displaying similar documents to “Connectedness in monotone spaces.”

Monotone normality and extension of functions

Ian Stares (1995)

Commentationes Mathematicae Universitatis Carolinae

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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.