Some Isomorphism Theorems for MVD-algebras

TL;DR

This paper reformulates existing duality theorems for locally compact Hausdorff spaces using MVD-algebras, providing a new perspective and potentially simplifying the duality framework.

Contribution

It introduces a new formulation of duality theorems employing MVD-algebras and their morphisms, replacing local contact algebras.

Findings

Duality theorems expressed via MVD-algebras

Equivalent formulations using MVD-algebras and morphisms

Simplified representation of duality results

Abstract

In three recaent papers of G. Dimov, many Stone-type duality theorems for the category of locally compact Hausdorff spaces and continuous maps and some of its subcategories were proved. The dual objects in all these theorems are the local contact algebras. In a paper of D. Vakarelov, G. Dimov, I. Duntsch, and B. Bennett, the notion of an MVD-algebra was introduced and it was shown that it is equivalent to the notion of a local contact algebra. In this paper we express the duality theorems mentioned above in a new form using MVD-algebras and appropriate morphisms between them instead of local contact algebras and the respective morphisms.