# name
A generalization of de Vries duality to closed relations between compact Hausdorff spaces

# metadata.dc.description.abstract[].value
Stone duality generalizes to an equivalence between the categories StoneR of Stone
spaces and closed relations and BAS of boolean algebras and subordination relations.
Splitting equivalences in StoneR yields a category that is equivalent to the category
KHausR of compact Hausdorff spaces and closed relations. Similarly, splitting
equivalences in BAS yields a category that is equivalent to the category DeVS of
de Vries algebras and compatible subordination relations. Applying the machinery
of allegories then gives that KHausR is equivalent to DeVS, thus resolving a problem
recently raised in the literature.
The equivalence between KHausR and DeVS further restricts to an equivalence
between the category KHaus of compact Hausdorff spaces and continuous functions
and the wide subcategory DeVF of DeVS 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.

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Topology and its Applications, 2023, vol. 337

# metadata.dc.rights[].value
cc-by-nc-nd (c) Abbadini, Marco et al., 2023

# metadata.dc.source[].value
Articles publicats en revistes (Filosofia)

# metadata.dc.title[].value
A generalization of de Vries duality to closed relations between compact Hausdorff spaces