1. McKinsey-Tarski algebras: An alternative pointfree approach to topology.
- Author
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Bezhanishvili, Guram and Raviprakash, Ranjitha
- Subjects
- *
ALGEBRA , *TOPOLOGY , *DUALITY theory (Mathematics) , *AXIOMS , *TOPOLOGICAL spaces - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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