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Amsterdam Properties of $C_p(X)$ Imply Discreteness of $X$

  Published:2008-12-01
 Printed: Dec 2008
  • D. J. Lutzer
  • J. van Mill
  • V. V. Tkachuk
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Abstract

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 regular filterbase, subcompact space, function space, discrete space
MSC Classifications: 54B10, 54C05, 54D30 show english descriptions Product spaces
Continuous maps
Compactness
54B10 - Product spaces
54C05 - Continuous maps
54D30 - Compactness
 

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