ﻻ يوجد ملخص باللغة العربية
Propounding a general categorical framework for the extension of dualities, we present a new proof of the de Vries Duality Theorem for the category $bf KHaus$ of compact Hausdorff spaces and their continuous maps, as an extension of a restricted Stone duality. Then, applying a dualization of the categorical framework to the de Vries duality, we give an alternative proof of the extension of the de Vries duality to the category $bf Tych$ of Tychonoff spaces that was provided by Bezhanishvili, Morandi and Olberding. In the process of doing so, we obtain new duality theorems for both categories, $bf{KHaus}$ and $bf Tych$.
Under a general categorical procedure for the extension of dual equivalences as presented in this papers predecessor, a new algebraically defined category is established that is dually equivalent to the category $bf LKHaus$ of locally compact Hausdor
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
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
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.