2016/04/20 by Guram Bezhanishvili, Nick Bezhanishvili, Sumit Sourabh +1 · 1 citation
Computer Science · Mathematics · #Advanced Algebra and Logic #Homotopy and Cohomology in Algebraic Topology #Logic, Reasoning, and Knowledge
paper · pdf · doi:10.1007/s10485-016-9434-2
openalex publication_date 2016/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
By de Vries duality, the category of compact Hausdorff spaces is dually equivalent to the category of de Vries algebras (complete Boolean algebras endowed with a proximity-like relation). We provide an alternative “modal-like” duality by introducing the concept of a Gleason space, which is a pair ( X , R ), where X is an extremally disconnected compact Hausdorff space and R is an irreducible equivalence relation on X . Our main result states that the category of Gleason spaces is equivalent to the category of compact Hausdorff spaces, and is dually equivalent to the category of de Vries algebras.