2022/01/12 by G. Bezhanishvili, Bezhanishvili, G., L. Carai +5
Computer Science · Mathematics · #Advanced Algebra and Logic #Homotopy and Cohomology in Algebraic Topology #Logic, programming, and type systems
paper · pdf · doi:10.48550/arxiv.2201.04423
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.