Topological representation of contact lattices

Authors:
Ivo Düntsch;Wendy MacCaull;Dimiter Vakarelov;Michael Winter
Affiliations:
Department of Computer Science, Brock University, St. Catharines, ON, Canada;Department of Mathematics, Statistics and Computer Science, St. Francis Xavier University, Antigonish, NS, Canada;Department of Mathematical Logic, Sofia University, Sofia, Bulgaria;Department of Computer Science, Brock University, St. Catharines, ON, Canada
Venue:
RelMiCS'06/AKA'06 Proceedings of the 9th international conference on Relational Methods in Computer Science, and 4th international conference on Applications of Kleene Algebra
Year:
2006

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Abstract

The theory of Boolean contact algebras has been used to represent a region based theory of space. Some of the primitives of Boolean algebras are not well motivated in that context. One possible generalization is to drop the notion of complement, thereby weakening the algebraic structure from Boolean algebra to distributive lattice. The main goal of this paper is to investigate the representation theory of that weaker notion, i.e., whether it is still possible to represent each abstract algebra by a substructure of the regular closed sets of a suitable topological space with the standard Whiteheadean contact relation.