#### 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.