1. A generalization of de Vries duality to closed relations between compact Hausdorff spaces.
- Author
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Abbadini, Marco, Bezhanishvili, Guram, and Carai, Luca
- Subjects
- *
HAUSDORFF spaces , *COMPACT spaces (Topology) , *FUNCTION spaces , *RELATION algebras , *BOOLEAN algebra - Abstract
Stone duality generalizes to an equivalence between the categories Stone R of Stone spaces and closed relations and BA S of boolean algebras and subordination relations. Splitting equivalences in Stone R yields a category that is equivalent to the category KHaus R of compact Hausdorff spaces and closed relations. Similarly, splitting equivalences in BA S yields a category that is equivalent to the category De V S of de Vries algebras and compatible subordination relations. Applying the machinery of allegories then gives that KHaus R is equivalent to De V S , thus resolving a problem recently raised in the literature. The equivalence between KHaus R and De V S further restricts to an equivalence between the category KHaus of compact Hausdorff spaces and continuous functions and the wide subcategory De V F of De V S whose morphisms satisfy additional conditions. This yields an alternative to de Vries duality. One advantage of this approach is that composition of morphisms is usual relation composition. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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