Back to Search
Start Over
A generalization of de Vries duality to closed relations between compact Hausdorff spaces.
- Source :
-
Topology & Its Applications . Sep2023, Vol. 337, pN.PAG-N.PAG. 1p. - Publication Year :
- 2023
-
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]
Details
- Language :
- English
- ISSN :
- 01668641
- Volume :
- 337
- Database :
- Academic Search Index
- Journal :
- Topology & Its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 169787412
- Full Text :
- https://doi.org/10.1016/j.topol.2023.108641