Article ID Journal Published Year Pages File Type
432320 The Journal of Logic and Algebraic Programming 2008 17 Pages PDF
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.

Related Topics
Physical Sciences and Engineering Computer Science Computational Theory and Mathematics