PP-2014-23: Subordinations, closed relations, and compact Hausdorff spaces

PP-2014-23: Bezhanishvili, Guram and Bezhanishvili, Nick and Sourabh, Sumit and Venema, Yde (2014) Subordinations, closed relations, and compact Hausdorff spaces. [Report]

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Abstract

We introduce the concept of a subordination, which is dual to the well-known concept of a precontact on a Boolean algebra. We develop a full categorical duality between Boolean algebras with a subordination and Stone spaces with a closed relation, thus generalizing the results of [14]. We introduce the concept of an irreducible equivalence relation, and that 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. We prove 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, thus providing a ~modal-like~ alternative to de Vries duality.

Item Type: Report
Report Nr: PP-2014-23
Series Name: Prepublication (PP) Series
Year: 2014
Uncontrolled Keywords: Duality, de Vries algebras, Gleason covers, Stone spaces, Modal Logic
Depositing User: Nick Bezhanishvili
Date Deposited: 12 Oct 2016 14:37
Last Modified: 12 Oct 2016 14:37
URI: https://eprints.illc.uva.nl/id/eprint/511

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