$K_{W}$ Does Not Imply $K_{W}^{*}$

Carlos R. Borges

Abstract: We prove that the cyclic monotonically normal space $T$ of M.E. Rudin is a $K_{W}$-space which is not a $K_{W}^{*}$-space. This answers a question in [3]. In order to do this, we first prove that if a space $X$ has $D^{*}(\R;\leq)$ then $X$ is a $K_{W}$-space (it is well known that $X$ is also a $K_{1}$-space; this does not necessarily mean that $X$ is a $K_{1W}$-space.).

Keywords: $K_{W}$-space; $K_{W}^{*}$-space; $K_{1}$-space.

Classification (MSC2000): 54C30.; 54C20.

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