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.
Keywords: monotonically normal, extension of functions, Tietze, Urysohn, $K_1$, $K_0$
AMS Subject Classification: Primary 54C20; Secondary 54E