PORTUGALIAE MATHEMATICA Vol. 57, No. 3, pp. 255258 (2000) 

$K_{W}$ Does Not Imply $K_{W}^{*}$Carlos R. BorgesDepartment of Mathematics, University of California, Davis,California 956168633  USA 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. Full text of the article:
Electronic version published on: 31 Jan 2003. This page was last modified: 27 Nov 2007.
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