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. © Springer-Verlag Berlin Heidelberg 2006.
CITATION STYLE
Düntsch, I., MacCaull, W., Vakarelov, D., & Winter, M. (2006). Topological representation of contact lattices. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4136 LNCS, pp. 135–147). Springer Verlag. https://doi.org/10.1007/11828563_9
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