McKinsey-Tarski Algebras: An alternative pointfree approach to topology

Guram Bezhanishvili; Ranjitha Raviprakash

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arXiv · 2306.13715

McKinsey-Tarski Algebras: An alternative pointfree approach to topology

Guram Bezhanishvili·Ranjitha Raviprakash

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Abstract

McKinsey and Tarski initiated the study of interior algebras. We propose complete interior algebras as an alternative pointfree approach to topology. We term these algebras McKinsey-Tarski algebras or simply MT-algebras. Associating with each MT-algebra the lattice of its open elements defines a functor from the category of MT-algebras to the category of frames, which we study in depth. We also study the dual adjunction between the categories of MT-algebras and topological spaces, and show that MT-algebras provide a faithful generalization of topological spaces. Our main emphasis is on developing a unified approach to separation axioms in the language of MT-algebras, which generalizes separation axioms for both topological spaces and frames.

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BibTeX RIS

Guram Bezhanishvili, Ranjitha Raviprakash. 2023-06-23. McKinsey-Tarski Algebras: An alternative pointfree approach to topology. https://arxiv.org/abs/2306.13715

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