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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 zero-dimensional Hausdorff spaces and continuous maps. Now we derive from them the extension of the Stone Duality Theorem to the category BooleSp of zero-dimensional locally compact Hausdorff spaces and continuous maps obtained in [G. Dimov, Some generalizations of the Stone Duality Theorem, Publicationes Mathematicae Debrecen, 80 (2012), 255--293], as well as two new duality theorems for the category BooleSp.
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
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.
Applying a general categorical construction for the extension of dualities, we present a new proof of the Fedorchuk duality between the category of compact Hausdorff spaces with their quasi-open mappings and the category of complete normal contact al
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
We construct a canonical extension for strong proximity lattices in order to give an algebraic, point-free description of a finitary duality for stably compact spaces. In this setting not only morphisms, but also objects may have distinct pi- and sigma-extensions.