Apartness spaces as a framework for constructive topology

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Annals of Pure and Applied Logic 119 (1-3):61-83 (2003)
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Abstract

An axiomatic development of the theory of apartness and nearness of a point and a set is introduced as a framework for constructive topology. Various notions of continuity of mappings between apartness spaces are compared; the constructive independence of one of the axioms from the others is demonstrated; and the product apartness structure is defined and analysed.

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10.1016/s0168-0072(02)00033-7

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Citations of this work

Two subcategories of apartness spaces.Hajime Ishihara - 2012 - Annals of Pure and Applied Logic 163 (2):132-139.
Quasi-apartness and neighbourhood spaces.Hajime Ishihara, Ray Mines, Peter Schuster & Luminiţa Vîţă - 2006 - Annals of Pure and Applied Logic 141 (1):296-306.
Product a-frames and proximity.Douglas S. Bridges - 2008 - Mathematical Logic Quarterly 54 (1):12-26.
A proof–technique in uniform space theory.Douglas Bridges & Luminiţa Vîţă - 2003 - Journal of Symbolic Logic 68 (3):795-802.

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References found in this work

Constructive Analysis.Errett Bishop & Douglas Bridges - 1987 - Journal of Symbolic Logic 52 (4):1047-1048.
Constructive set theory.John Myhill - 1975 - Journal of Symbolic Logic 40 (3):347-382.
Continuity and nondiscontinuity in constructive mathematics.Hajime Ishihara - 1991 - Journal of Symbolic Logic 56 (4):1349-1354.

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