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A Duality for Boolean Contact Algebras
Raskin, Julien; Hansoul, Georges
2017Topology, Algebra, and Categories in Logic 2017
 

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Keywords :
duality; contact relations
Abstract :
[en] The well-known de Vries duality, established by H. de Vries in 1962, states that the category of compact Hausdorff spaces is dually equivalent to that of de Vries algebras. The notion of Boolean contact algebra (BCA) was developed independently in the context of region-based theory of space. Düntsch and Winter established a representation theorem for BCAs, showing that every BCA is isomorphic to a dense subalgebra of the regular closed sets of a T_1 weakly regular space. It appears that BCAs are a direct generalization of de Vries algebras, and that the representation theorem for complete BCAs generalizes de Vries duality for objects. During a conference, Vakarelov raised the question of dualizing morphisms. We answer this question using concepts similar to those of modal logic's neighborhood semantics.
Disciplines :
Mathematics
Author, co-author :
Raskin, Julien ;  Université de Liège > Département de mathématique > Mathématiques discrètes
Hansoul, Georges ;  Université de Liège > Département de mathématique > Algèbre et logique
Language :
English
Title :
A Duality for Boolean Contact Algebras
Publication date :
2017
Event name :
Topology, Algebra, and Categories in Logic 2017
Event organizer :
Institute of Computer Science, Czech Academy of Sciences - Faculty of Arts, Charles University
Event place :
Prague, Czechia
Event date :
26 June 2017 - 30 June 2017
Audience :
International
Available on ORBi :
since 31 May 2017

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