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Amsterdam Properties of Cp(X) Imply Discreteness of X

Published online by Cambridge University Press:  20 November 2018

D. J. Lutzer ,
J. van Mill  and
V. V. Tkachuk
D. J. Lutzer
Affiliation:
Mathematics Department, College of William and Mary, Williamsburg, VA 23187-8795, U.S.A.. e-mail: lutzer@math.wm.edu
J. van Mill
Affiliation:
Department of Mathematics, Vrije Universiteit, HV Amsterdam, The Netherlands. e-mail: vanmill@cs.vu.nl
V. V. Tkachuk
Affiliation:
Departamento de Matematicas, Universidad Autónoma Metropolitana, Mexico, D.F.. e-mail: vova@xanum.uam.mx
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Abstract

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We prove, among other things, that if ${{C}_{p}}\left( X \right)$ 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

54B1054C0554D30regular filterbasesubcompact spacefunction spacediscrete space
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 51 , Issue 4 , 01 December 2008 , pp. 570 - 578
Copyright
Copyright © Canadian Mathematical Society 2008

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