Topological Representation of Precontact Algebras

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


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].


Topological Space Boolean Algebra Representation Theorem Bijective Correspondence Topological Representation 
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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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