Priestley perspective on pointfree topology

2025/11/03 by Bezhanishvili, Guram, Melzer, Sebastian D.
#06D22 #06D50 #06E15 #18F70 #54D10 #54D15 #54D30 #54D45 #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO)

paper · doi:10.48550/arxiv.2511.01426

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.

Citations

• Maximal d-spectra via Priestley duality
• Maximality Principles in Modal Logic and the Axiom of Choice
• Degrees of join-distributivity via Bruns-Lakser towers
• Local compactness in MT-algebras
• Algebraic Frames in Priestley duality
• A New Proof of the Joyal-Tierney Theorem
• Connecting generalized Priestley duality to Hofmann-Mislove-Stralka duality
• The Frame of Nuclei of an Alexandroff Space
• When is the frame of nuclei spatial: A new approach
• Stone duality, topological algebra, and recognition

Related

• Algebraic Frames in Priestley duality
• Pointfree topology and constructive mathematics
• A New Proof of the Joyal-Tierney Theorem
• Lattice-Free and Point-Free: Vickers Duality for Subbases of Stably Locally Compact Spaces
• Remarks on Hyperspaces for Priestley Spaces