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Amsterdam Properties of $C_p(X)$ Imply Discreteness of $X$ |
Canad. Math. Bull. 51(2008), 570-578
Published:2008-12-01
Printed: Dec 2008
Printed: Dec 2008
- D. J. Lutzer
- J. van Mill
- V. V. Tkachuk
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 |
| MSC Classifications: |
54B10 - Product spaces 54C05 - Continuous maps 54D30 - Compactness |