Priestley perspective on pointfree topology

2025/11/03 by Guram Bezhanishvili, Bezhanishvili, Guram, S. Melzer +2 · 1 voice
Decision Sciences · Mathematics · #06D22 #06D50 #06E15 #18F70 #54D10 #54D15 #54D30 #54D45 #Advanced Topology and Set Theory #FOS: Mathematics #Fuzzy and Soft Set Theory #General Topology (math.GN) #Logic (math.LO) #Rings, Modules, and Algebras #math.GN #math.LO

paper · pdf · doi:10.48550/arxiv.2511.01426

openalex publication_date 2025/11/03 · arxiv published 2025/11/03 · arxiv updated 2025/11/03 · openalex created_date 2025/11/06 · openalex updated_date 2026/07/28

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

Discussions

• Guram Bezhanishvili, Sebastian D. Melzer: Priestley perspective on pointfree topology https://arxiv.org/abs/2511.01426 https://arxiv.org/pdf/2511.01426 https://arxiv.org/html/2511.01426 [bsky, 0 points, 0 comments]

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• Pointfree topology and constructive mathematics
• A New Proof of the Joyal-Tierney Theorem
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• Remarks on Hyperspaces for Priestley Spaces