Topological Representation of Contact Lattices

  • Ivo Düntsch
  • Wendy MacCaull
  • Dimiter Vakarelov
  • Michael Winter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4136)


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.


Topological Space Boolean Algebra Distributive Lattice Contact Structure Topological Representation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Ivo Düntsch
    • 1
  • Wendy MacCaull
    • 2
  • Dimiter Vakarelov
    • 3
  • Michael Winter
    • 1
  1. 1.Department of Computer ScienceBrock UniversitySt. CatharinesCanada
  2. 2.Department of Mathematics, Statistics and Computer ScienceSt. Francis Xavier UniversityAntigonishCanada
  3. 3.Department of Mathematical LogicSofia UniversitySofiaBulgaria

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