In mathematics, duality theory for distributive lattices provides three different (but closely related) 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,[1] generalizes the well-known Stone duality between Stone spaces and Boolean algebras.
Let be a bounded distributive lattice, and let denote the set of prime filters of . For each, let