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].
This paper was supported by the project NIP-123 “Applied Logics and Topological Structures” of the Bulgarian Ministry of Education and Science.
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Dimov, G., Vakarelov, D. (2006). Topological Representation of Precontact Algebras. In: MacCaull, W., Winter, M., Düntsch, I. (eds) Relational Methods in Computer Science. RelMiCS 2005. Lecture Notes in Computer Science, vol 3929. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11734673_1
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DOI: https://doi.org/10.1007/11734673_1
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