Priestley perspective on pointfree topology

TL;DR

This paper explores how Priestley duality offers new insights into pointfree topology by examining key concepts like spatiality and compactness from a duality perspective.

Contribution

It provides a Priestley perspective on fundamental notions in pointfree topology, offering fresh insights into classic results.

Findings

New perspective on spatiality and sublocales

Reinterpretation of separation axioms

Enhanced understanding of compactness and local compactness

Abstract

Priestley duality has diverse applications in various branches of mathematics. In this survey, we discuss its usefulness in pointfree topology. This is done by providing Priestley perspective on several key notions, including spatiality, sublocales, separation axioms, compactness, and local compactness. This approach yields a new perspective on a number of classic results in pointfree topology.