Local Compactness in MT-Algebras - Bezhanishvili, Guram; Raviprakash, Ranjitha (Topology Proceedings, 2024)
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, which we use to 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.