Choice-Free de Vries Duality

Guillaume Massas

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arXiv · 2203.09667

Choice-Free de Vries Duality

Guillaume Massas

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Abstract

De Vries Duality generalizes Stone duality between Boolean algebras and Stone spaces to a duality between de Vries algebras (complete Boolean algebras equipped with a subordination relation satisfying some axioms) and compact Hausdorff spaces. This duality allows for an algebraic approach to region-based theories of space that differs from point-free topology. Building on the recent choice-free version of Stone duality developed by Bezhanishvili and Holliday, this paper establishes a choice-free duality between de Vries algebras and a category of de Vries spaces. We also investigate connections with the Vietoris functor on the category of compact Hausdorff spaces and with the category of compact regular frames in point-free topology, and we provide an alternative, choice-free topological semantics for the Symmetric Strict Implication Calculus of Bezhanishvili et al.

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BibTeX RIS

Guillaume Massas. 2022-03-18. Choice-Free de Vries Duality. https://arxiv.org/abs/2203.09667

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