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What (who) is distributive lattice - definition
Distributive lattice
![[[Young's lattice]]](https://commons.wikimedia.org/wiki/Special:FilePath/Young's lattice.svg?width=200 "[[Young's lattice]]")
LATTICE IN WHICH THE OPERATIONS OF JOIN AND MEET DISTRIBUTE OVER EACH OTHER
Distribute lattice; Distributive lattice/Proofs; Free distributive lattice
In mathematics, a distributive lattice is a lattice in which the operations of join and meet distribute over each other. The prototypical examples of such structures are collections of sets for which the lattice operations can be given by set union and intersection.
distributive lattice
LATTICE IN WHICH THE OPERATIONS OF JOIN AND MEET DISTRIBUTE OVER EACH OTHER
Distribute lattice; Distributive lattice/Proofs; Free distributive lattice
<theory> A lattice for which the least upper bound (lub)
and greatest lower bound (glb) operators distribute over one
another so that
a lub (b glb c) == (a lub c) glb (a lub b)
and vice versa.
("lub" and "glb" are written in LateX as sqcup and
sqcap).
(1998-11-09)
Duality theory for distributive lattices
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.
