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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