Compactness in MT-algebras

Ponente(s): Ranjitha Raviprakash Amrutha, Guram Bezhanishvili

A McKinsey-Tarski algebra (MT-algebra) is a complete boolean algebra equipped with an interior operator. This concept was introduced in [1], where we argued that MT-algebras provide an alternative point-free approach to topology. In this talk, we generalize the classic topological notions of compactness and local compactness to the setting of MT-algebras. This provides a new look at the duality theory in pointfree topology for such well-known categories of frames as continuous frames, stably continuous frames, and compact regular frames. References [1] G. Bezhanishvili and R. Raviprakash. McKinsey-Tarski algebras: An alternative pointfree approach to topology. arXiv:2306.13715, 2023. Submitted.