2024/01/02 by Guram Bezhanishvili, Bezhanishvili, Guram, Ranjitha Raviprakash +1 · 2 citations
Computer Science · Mathematics · #06D22 #18F60 #18F70 #54D30 #54D45 #Advanced Algebra and Logic #Advanced Topics in Algebra #FOS: Mathematics #General Topology (math.GN) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2401.01015
openalex publication_date 2024/01/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In our previous work, we introduced McKinsey-Tarski algebras (MT-algebras for short) as an alternative pointfree approach to topology. Here we study local compactness in MT-algebras. We establish the Hofmann-Mislove theorem for sober MT-algebras, using which we develop the MT-algebra versions of such well-known dualities in pointfree topology as Hofmann-Lawson, Isbell, and Stone dualities. This yields a new perspective on these classic results.