A Study of $K_{W}$-spaces and $K_{W}^{*}$-spaces

Carlos R. Borges

Abstract: Further study of $K_{W}$-spaces leads to the introduction of $K_{W}^{*}$-spaces. We obtain a characterization of $K_{W}^{*}$-spaces in terms of continuous real-valued functions which is dual to a characterization of $K_{0}$-spaces. We also get two characterizations of $K_{W}$-spaces, one of which exhibits their remarkable similarities with $K_{1}$-spaces; a consequence of the latter characterization is that $K_{W}$-spaces are collectionwise normal.

Keywords: $K_{W}$-spaces; $K_{W}^{*}$-spaces; usc- and lsc-extenders; continuous extensions.

Classification (MSC2000): 54C20; 54C30

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