20 June 2018, Algebra|Coalgebra Seminar, Guram Bezhanishvili

Abstract:
De Vries duality yields a dual equivalence between the category of compact Hausdorff spaces and a category of complete Boolean algebras with a proximity relation on them, known as de Vries algebras. I will report on a recent joint work with Pat Morandi and Bruce Olberding on how to extend de Vries duality to completely regular spaces by replacing the category of de Vries algebras with certain extensions of de Vries algebras. This we do by first formulating a duality between compactifications and de Vries extensions, and then specializing to the extensions that correspond to Stone-Čech compactifications.