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- Birkhoff's_representation_theorem abstract "This is about lattice theory. For other similarly named results, see Birkhoff's theorem (disambiguation).In mathematics, Birkhoff's representation theorem for distributive lattices states that the elements of any finite distributive lattice can be represented as finite sets, in such a way that the lattice operations correspond to unions and intersections of sets. The theorem can be interpreted as providing a one-to-one correspondence between distributive lattices and partial orders, between quasi-ordinal knowledge spaces and preorders, or between finite topological spaces and preorders. It is named after Garrett Birkhoff, who published a proof of it in 1937.The name “Birkhoff's representation theorem” has also been applied to two other results of Birkhoff, one from 1935 on the representation of Boolean algebras as families of sets closed under union, intersection, and complement (so-called fields of sets, closely related to the rings of sets used by Birkhoff to represent distributive lattices), and Birkhoff's HSP theorem representing algebras as products of irreducible algebras. Birkhoff's representation theorem has also been called the fundamental theorem for finite distributive lattices.".
- Birkhoff's_representation_theorem thumbnail Birkhoff120.svg?width=300.
- Birkhoff's_representation_theorem wikiPageExternalLink 1183510977.
- Birkhoff's_representation_theorem wikiPageID "20489385".
- Birkhoff's_representation_theorem wikiPageRevisionID "603782303".
- Birkhoff's_representation_theorem hasPhotoCollection Birkhoff's_representation_theorem.
- Birkhoff's_representation_theorem subject Category:Lattice_theory.
- Birkhoff's_representation_theorem subject Category:Theorems_in_algebra.
- Birkhoff's_representation_theorem type Abstraction100002137.
- Birkhoff's_representation_theorem type Communication100033020.
- Birkhoff's_representation_theorem type Message106598915.
- Birkhoff's_representation_theorem type Proposition106750804.
- Birkhoff's_representation_theorem type Statement106722453.
- Birkhoff's_representation_theorem type Theorem106752293.
- Birkhoff's_representation_theorem type TheoremsInAlgebra.
- Birkhoff's_representation_theorem comment "This is about lattice theory. For other similarly named results, see Birkhoff's theorem (disambiguation).In mathematics, Birkhoff's representation theorem for distributive lattices states that the elements of any finite distributive lattice can be represented as finite sets, in such a way that the lattice operations correspond to unions and intersections of sets.".
- Birkhoff's_representation_theorem label "Birkhoff's representation theorem".
- Birkhoff's_representation_theorem sameAs m.04zw656.
- Birkhoff's_representation_theorem sameAs Q17005116.
- Birkhoff's_representation_theorem sameAs Q17005116.
- Birkhoff's_representation_theorem sameAs Birkhoff's_representation_theorem.
- Birkhoff's_representation_theorem wasDerivedFrom Birkhoff's_representation_theorem?oldid=603782303.
- Birkhoff's_representation_theorem depiction Birkhoff120.svg.
- Birkhoff's_representation_theorem isPrimaryTopicOf Birkhoff's_representation_theorem.
