Apartness, compactness and nearness

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Abstract

We investigate constructively a pre-apartness structure that is classically important in the characterisation of compact proximity spaces, and that may help identify a good constructive notion of compactness for not-necessarily-uniform apartness spaces. In addition, we produce what may be the right notion of “nearness” in the theory of apartness spaces.

Keywords

Constructive
Apartness
Totally bounded
Compact
Near

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Present address: A.C. Nielsen, PO Box 11346, Manners Street, Wellington 6142, New Zealand.