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1. CMB 2008 (vol 51 pp. 570)
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Amsterdam Properties of $C_p(X)$ Imply Discreteness of $X$ We prove, among other things, that if $C_p(X)$ is
subcompact in the sense of de Groot, then the space $X$ is
discrete. This generalizes a series of previous results on
completeness properties of function spaces.
Keywords:regular filterbase, subcompact space, function space, discrete space Categories:54B10, 54C05, 54D30 |