Vietoris endofunctor for closed relations and its de Vries dual
(2024) Topology Proceedings — Vol. 64, p. 213-250 (2024)
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- Abstract
- We generalize the classic Vietoris endofunctor to the category of compact Hausdorff spaces and closed relations. The lift of a closed relation is done by generalizing the construction of the Egli-Milner order. We describe the dual endofunctor on the category of de Vries algebras and subordinations. This is done in several steps, rst by generalizing the known endofunctor on the category of boolean algebras and boolean homomorphisms, then lifting it up to S5-subordination algebras, and nally using MacNeille completions to further lift it to de Vries algebras. Among other things, this yields a generalization of Johnstone's pointfree construction of the Vietoris endofunctor to the category of compact regular frames and preframe homomorphisms.
- Affiliations
University of Birmingham New Mexico State University Università degli Studi di Milano
Citations
Abbadini, M., Bezhanishvili, G., & Carai, L. (2024). Vietoris endofunctor for closed relations and its de Vries dual. Topology Proceedings, 64, 213-250. (Original work published 2024)