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Remarks on hyperspaces for Priestley spaces

Published: 17 January 2023 Publication History

Abstract

The Vietoris space of a Stone space plays an important role in the coalgebraic approach to modal logic. When generalizing this to positive modal logic, there is a variety of relevant hyperspace constructions based on various topologies on a Priestley space and mechanisms to topologize the hyperspace of closed sets. A number of authors considered hyperspaces of Priestley spaces and their application to the coalgebraic approach to positive modal logic. A mixture of techniques from category theory, pointfree topology, and Priestley duality have been employed. Our aim is to provide a unifying approach to this area of research relying only on a basic familiarity with Priestley duality and related free constructions of distributive lattices.

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            cover image Theoretical Computer Science
            Theoretical Computer Science  Volume 943, Issue C
            Jan 2023
            267 pages

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            Elsevier Science Publishers Ltd.

            United Kingdom

            Publication History

            Published: 17 January 2023

            Author Tags

            1. Hyperspace
            2. Hit-or-miss topology
            3. Vietoris space
            4. Coalgebra
            5. Priestley space
            6. Distributive lattice
            7. Positive modal logic

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