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We prove a new duality theorem for the category of precontact algebras which implies the Stone Duality Theorem, its connected version obtained in arXiv:1508.02220v3, 1-44 (to appear in Topology Appl.), the recent duality theorems of Bezhanishvili, G., Bezhanishvili, N., Sourabh, S., Venema, Y. and Goldblatt, R. and Grice, M, and some new duality theorems for the category of contact algebras and for the category of complete contact algebras.
The notions of a {em 2-precontact space}/ and a {em 2-contact space}/ are introduced. Using them, new representation theorems for precontact and contact algebras are proved. It is shown that there are bijective correspondences between such kinds of a
In [G. Dimov and E. Ivanova-Dimova, Two extensions of the Stone Duality to the category of zero-dimensional Hausdorff spaces, arXiv:1901.04537v4, 1--33], extending the Stone Duality Theorem, we proved two duality theorems for the category ZDHaus of z
Extending the Stone Duality Theorem, we prove two duality theorems for the category ZHaus of zero-dimensional Hausdorff spaces and continuous maps. Both of them imply easily the Tarski Duality Theorem, as well as two new duality theorems for the cate
This paper is a contribution to understanding what properties should a topological algebra on a Stone space satisfy to be profinite. We reformulate and simplify proofs for some known properties using syntactic congruences. We also clarify the role of
We give a bound on the spectral radius of a graph implying a quantitative version of the Erdos-Stone theorem.