Extensions of dualities and a new approach to the Fedorchuk duality

TL;DR

This paper introduces a new categorical approach to extend dualities and provides a novel proof of the Fedorchuk duality linking compact Hausdorff spaces with contact algebras, enhancing understanding of their categorical relationships.

Contribution

It develops a general categorical construction for extending dualities and applies it to give a new proof of the Fedorchuk duality, connecting topological spaces and algebraic structures.

Findings

New categorical construction for extending dualities

Alternative proof of Fedorchuk duality

Deeper insight into the relationship between spaces and algebras

Abstract

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 algebras with suprema-preserving Boolean homomorphisms which reflect the contact relation.