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Topological Representation of Precontact Algebras

  • Georgi Dimov
  • Dimiter Vakarelov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3929)

Abstract

The notions of 2-precontact and 2-contact spaces as well as of extensional (and other kinds) 3-precontact and 3-contact spaces are introduced. Using them, new representation theorems for precontact and contact algebras (satisfying some additional axioms) are proved. They incorporate and strengthen both the discrete and topological representation theorems from [3, 1, 2, 4, 10]. It is shown that there are bijective correspondences between such kinds of algebras and such kinds of spaces. In particular, such a bijective correspondence for the RCC systems of [8] is obtained, strengthening in this way the previous representation theorems from [4, 1].

Keywords

Topological Space Boolean Algebra Representation Theorem Bijective Correspondence Topological Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Georgi Dimov
    • 1
  • Dimiter Vakarelov
    • 1
  1. 1.Faculty of Mathematics and Computer ScienceSofia UniversityUSA

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