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The Stone-Čech compactification and weakly Fréchet spaces

Published online by Cambridge University Press:  17 April 2009

Deborah M. King  and
Sidney A. Morris
Deborah M. King
Affiliation:
The University of New England Armidale, NSW 2351, Australia
Sidney A. Morris
Affiliation:
The University of New England Armidale, NSW 2351, Australia
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Abstract

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This paper resulted from an attempt to answer questions like: does βP have a subspace homeomorphic to βQ and does βQ have a subspace homeomorphic to P, where P denotes the space of all irrational numbers. These questions are answered in the negative by providing the appropriate machinery which can also be applied to other examples. En route we prove that weakly Fréchet realcompact spaces have homeomorphic Stone-Čech compactifications if and only if they are homeomorphic.

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 42 , Issue 2 , October 1990 , pp. 349 - 352
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Engelking, R., General Topology (Polish Scientific Publishers, Warsaw, 1977).Google Scholar
[2]Gillman, L. and Jerison, M., Rings of Continuous Functions (Springer-Verlag, Berlin, Heidelberg, New York, 1960).CrossRefGoogle Scholar
[3]Levy, R., ‘Compactification by the topologists sine curve’, Proc. Amer. Math. Soc. 63 (1977), 324–326.Google Scholar
[4]Walker, R.C., The Stone-Čech Compactification (Springer-Verlag, Berlin, Heidelberg, New York, 1974).CrossRefGoogle Scholar