Apartness, Topology, and Uniformity: a Constructive View

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Mathematical Logic Quarterly 48 (4):16-28 (2002)
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Abstract

The theory of apartness spaces, and their relation to topological spaces (in the point–set case) and uniform spaces (in the set–set case), is sketched. New notions of local decomposability and regularity are investigated, and the latter is used to produce an example of a classically metrisable apartness on R that cannot be induced constructively by a uniform structure.

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10.1002/1521-3870(200210)48:1

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Peter Schuster
University of Leeds

Citations of this work

Two subcategories of apartness spaces.Hajime Ishihara - 2012 - Annals of Pure and Applied Logic 163 (2):132-139.
Product a-frames and proximity.Douglas S. Bridges - 2008 - Mathematical Logic Quarterly 54 (1):12-26.

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