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In mathematics, a Priestley space is an ordered topological space with special properties. Priestley spaces are named after Hilary Priestley who introduced and investigated them. Priestley spaces play a fundamental role in the study of distributive lattices. In particular, there is a duality between the category of Priestley spaces and the category of bounded distributive lattices.
In mathematics, duality theory for distributive lattices provides three different representations of bounded distributive lattices via Priestley spaces, spectral spaces, and pairwise Stone spaces. This duality, which is originally also due to Marshall H. Stone, generalizes the well-known Stone duality between Stone spaces and Boolean algebras.
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References
- 1 2 Esakia, Leo (1974). "Topological Kripke models". Soviet Math. 15 (1): 147–151.
- ↑ Esakia, L (1985). "Heyting Algebras I. Duality Theory". Metsniereba, Tbilisi.
- ↑ Bezhanishvili, N. (2006). Lattices of intermediate and cylindric modal logics (PDF). Amsterdam Institute for Logic, Language and Computation (ILLC). ISBN 978-90-5776-147-8.
- ↑ see section 8.3 in * Dickmann, Max; Schwartz, Niels; Tressl, Marcus (2019). Spectral Spaces. New Mathematical Monographs. Vol. 35. Cambridge: Cambridge University Press. doi:10.1017/9781316543870. ISBN 9781107146723.