Local compactness in MT-algebras
General Topology
2024-01-03 v1
Abstract
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.
Cite
@article{arxiv.2401.01015,
title = {Local compactness in MT-algebras},
author = {Guram Bezhanishvili and Ranjitha Raviprakash},
journal= {arXiv preprint arXiv:2401.01015},
year = {2024}
}