Quasi-apartness and neighbourhood spaces

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Annals of Pure and Applied Logic 141 (1):296-306 (2006)
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Abstract

We extend the concept of apartness spaces to the concept of quasi-apartness spaces. We show that there is an adjunction between the category of quasi-apartness spaces and the category of neighbourhood spaces, which indicates that quasi-apartness is a more natural concept than apartness. We also show that there is an adjoint equivalence between the category of apartness spaces and the category of Grayson’s separated spaces

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10.1016/j.apal.2006.01.004

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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.
Apartness spaces and uniform neighbourhood structures.Douglas S. Bridges - 2016 - Annals of Pure and Applied Logic 167 (9):850-864.
A discrete duality between apartness algebras and apartness frames.Ivo Düntsch & Ewa Orlowska - 2008 - Journal of Applied Non-Classical Logics 18 (2-3):213-227.
Relating Bishopʼs function spaces to neighbourhood spaces.Hajime Ishihara - 2013 - Annals of Pure and Applied Logic 164 (4):482-490.

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References found in this work

Aspects of general topology in constructive set theory.Peter Aczel - 2006 - Annals of Pure and Applied Logic 137 (1-3):3-29.
Apartness spaces as a framework for constructive topology.Douglas Bridges & Luminiţa Vîţă - 2003 - Annals of Pure and Applied Logic 119 (1-3):61-83.
Apartness spaces as a framework for constructive topology.Douglas Bridges & Luminia Vî - 2003 - Annals of Pure and Applied Logic 119 (1-3):61-83.

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