A discrete duality between apartness algebras and apartness frames

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Journal of Applied Non-Classical Logics 18 (2-3):213-227 (2008)
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Abstract

Apartness spaces were introduced as a constructive counterpart to proximity spaces which, in turn, aimed to model the concept of nearness of sets in a metric or topological environment. In this paper we introduce apartness algebras and apartness frames intended to be abstract counterparts to the apartness spaces of (Bridges et al., 2003), and we prove a discrete duality for them.

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10.3166/jancl.18.213-227

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Author's Profile

Ewa Orlowska
Institute of Telecommunications and Information Technology

Citations of this work

Duality Results for (Co)Residuated Lattices.Chrysafis Hartonas - 2019 - Logica Universalis 13 (1):77-99.

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References found in this work

Distributive Lattices.Raymond Balbes & Philip Dwinger - 1977 - Journal of Symbolic Logic 42 (4):587-588.
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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