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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Apartness spaces as a framework for constructive topology.Douglas Bridges & Luminia Vî - 2003 - Annals of Pure and Applied Logic 119 (1-3):61-83.
Andou, Y., Church–Rosser property of a simple reduction for full first-order classical natural deduction (1–3) 225–237 Bridges, D. and Vıˆt-a, L., Apartness spaces as a framework for constructive topology (1–3) 61–83 Di Nasso, M. and Hrbacek, K., Combinatorial principles in. [REVIEW]Q. Feng, W. H. Woodin & M. Gitik - 2003 - Annals of Pure and Applied Logic 119 (1-3):295.
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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

Varieties of constructive mathematics.D. S. Bridges & Fred Richman - 1987 - New York: Cambridge University Press. Edited by Fred Richman.
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.
Constructive mathematics.Douglas Bridges - 2008 - Stanford Encyclopedia of Philosophy.
Foundations of Constructive Analysis.Errett Bishop - 1967 - New York, NY, USA: Mcgraw-Hill.

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