De Vries duality for compactifications and completely regular spaces
General Topology
2018-04-11 v1
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. We extend de Vries duality to completely regular spaces by replacing the category of de Vries algebras with certain extensions of de Vries algebras. This is done by first formulating a duality between compactifications and de Vries extensions, and then specializing to the extensions that correspond to Stone-\v{C}ech compactifications.
Cite
@article{arxiv.1804.03210,
title = {De Vries duality for compactifications and completely regular spaces},
author = {Guram Bezhanishvili and Patrick J. Morandi and Bruce Olberding},
journal= {arXiv preprint arXiv:1804.03210},
year = {2018}
}
Comments
25 pages, comments welcome