A new duality theorem for locally compact spaces

TL;DR

This paper introduces a new duality theorem for locally compact Hausdorff spaces, extending de Vries's classical duality for compact spaces by using a category with multi-valued morphisms.

Contribution

It establishes a duality between locally compact Hausdorff spaces and a new category with multi-valued morphisms, improving the understanding of their categorical relationships.

Findings

New duality theorem for locally compact spaces

Category with multi-valued morphisms is dual to HLC

Extends classical duality to broader class of spaces

Abstract

In 1962, H. de Vries proved a duality theorem for the category {\bf HC} of compact Hausdorff spaces and continuous maps. The composition of the morphisms of the dual category obtained by him differs from the set-theoretic one. Here we obtain a new category dual to the category {\bf HLC} of locally compact Hausdorff spaces and continuous maps for which the composition of the morphisms is a natural one but the morphisms are multi-valued maps.