Stone Duality for Preordered Topological Spaces

TL;DR

This paper establishes a duality theory connecting preordered topological spaces with algebraic structures, extending classical Stone duality to a broader context involving preorders and topology.

Contribution

It introduces a novel duality framework for preordered topological spaces, inspired by existing dualities for bitopological spaces and preordered sets.

Findings

Develops a Stone-like duality for preordered topological spaces

Extends classical duality theories to include preorders and topology

Provides a new perspective on the structure of preordered topological spaces

Abstract

A preordered topological space is a topological space with a preordering. We exhibit a Stone-like duality for preordered topological spaces, Inspired by a similar duality for bitopological spaces, due to Jung-Moshier and Jakl, and by a duality for preordered sets due to Bonsangue, Jacobs and Kok.