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arXiv · 2201.04423

De Vries powers and proximity Specker algebras

G. Bezhanishvili·L. Carai·P. Morandi·B. Olberding
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Abstract

By de Vries duality [9], the category ${\sf KHaus}$ of compact Hausdorff spaces is dually equivalent to the category ${\sf DeV}$ of de Vries algebras. In [5] an alternate duality for ${\sf KHaus}$ was developed, where de Vries algebras were replaced by proximity Baer-Specker algebras. The functor associating with each compact Hausdorff space a proximity Baer-Specker algebra was described by generalizing the notion of a boolean power of a totally ordered domain to that of a de Vries power. It follows that ${\sf DeV}$ is equivalent to the category ${\sf PBSp}$ of proximity Baer-Specker algebras. The equivalence is obtained by passing through ${\sf KHaus}$, and hence is not choice-free. In this paper we give a direct algebraic proof of this equivalence, which is choice-free. To do so, we give an alternate choice-free description of de Vries powers of a totally ordered domain.

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G. Bezhanishvili, L. Carai, P. Morandi, B. Olberding. 2022-01-12. De Vries powers and proximity Specker algebras. https://arxiv.org/abs/2201.04423

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