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Strong and Uniform Continuity – the Uniform Space Case

Published online by Cambridge University Press:  01 February 2010

Douglas Bridges  and
Luminiţa Vîţă
Douglas Bridges
Affiliation:
Department of Mathematics & Statistics, University of Canterbury, Private Bag 4800, Christchurch, New Zealandd.bridges@math.canterbury.ac.nz, http://www.math.canterbury.ac.nz/~mathdsb
Luminiţa Vîţă
Affiliation:
Department of Mathematics & Statistics, University of Canterbury, Private Bag 4800, Christchurch, New ZealandLuminita@Math.net, http://www.math.canterbury.ac.nz/~mathlsv

Abstract

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It is proved, within the constructive theory of apartness spaces, that a strongly continuous mapping from a totally bounded uniform space with a countable base of entourages to a uniform space is uniformly continuous. This lifts a result of Ishihara and Schuster from metric to uniform apartness spaces. The paper is part of a systematic development of computable topology using apartness as the fundamental notion.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 6 , 2003 , pp. 326 - 334
Copyright
Copyright © London Mathematical Society 2003

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