Distributive contact lattices: Topological representations

Abstract In order to provide a region based theory of space the notion of Boolean contact algebras has been used. However, not all of the Boolean connectives, in particular complement, are well motivated in that context. A suitable generalization of this theory is to drop the notion of complement, thereby weakening the algebraic structure from a Boolean algebra to a distributive lattice. In this paper we investigate the representation theory of that weaker notion in order to determine whether it is still possible to represent each abstract algebra as a substructure of the regular closed sets of a suitable topological space with the standard (Whiteheadean) contact relation. Furthermore, we consider additional axioms for contact and the representation of those structures in topological spaces with richer structure.

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