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A NOTE ON RELATIVE PSEUDOCOMPACTNESS IN THE CATEGORY OF FRAMES

Published online by Cambridge University Press:  22 May 2012

THEMBA DUBE*
Affiliation:
Department of Mathematical Sciences, University of South Africa, PO Box 392, 0003 Pretoria, South Africa (email: [email protected])
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Abstract

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A subspace S of Tychonoff space X is relatively pseudocompact in X if every fC(X) is bounded on S. As is well known, this property is characterisable in terms of the functor υ which reflects Tychonoff spaces onto the realcompact ones. A device which exists in the category CRegFrm of completely regular frames which has no counterpart in Tych is the functor which coreflects completely regular frames onto the Lindelöf ones. In this paper we use this functor to characterise relative pseudocompactness.

Type
Research Article
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

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