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A Note on H-Closed Extensions of a Product

Published online by Cambridge University Press:  20 November 2018

Anthony J. D’Aristotle
Anthony J. D’Aristotle*
Affiliation:
Brooklyn College of the City University of New York, Universidad Simón Bolίvar
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Any Hausdorff space X is a dense subspace of an H-closed space κX, called the Katětov extension of X, with the property that any H-closed extension Y of X is a continuous image of κX under a mapping which leaves X pointwise fixed [8], [10]. In [8], Liu has shown that the extensions κ(X×Y) and κX×κY of X × Y are equal iff (1) X or Y is finite, or (2) X and Y are H-closed. In this note, we examine whether homeomorphism of these two extensions implies equality. We give a condition under which homeomorphism implies equality and an example to show that this relation does not hold in general.

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 19 , Issue 2 , 01 June 1976 , pp. 149 - 153
Copyright
Copyright © Canadian Mathematical Society 1976

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