• other similarly named results, see Birkhoff's theorem (disambiguation). In mathematics, Birkhoff's representation theorem for distributive lattices states...
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  • Birkhoff's theorem may refer to several theorems named for the American mathematician George David Birkhoff: Birkhoff's theorem (relativity) Birkhoff's...
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  • is Cayley's original theorem. Wagner–Preston theorem is the analogue for inverse semigroups. Birkhoff's representation theorem, a similar result in order...
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  • over time. A generalization of Birkhoff's theorem is Kingman's subadditive ergodic theorem. Birkhoff–Khinchin theorem. Let ƒ be measurable, E(|ƒ|) < ∞...
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  • non-negative and less than or equal to 1. The Birkhoff–von Neumann theorem (often known simply as Birkhoff's theorem) states that the polytope B n {\displaystyle...
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  • algebra of endomorphisms of some finite-dimensional vector space. Birkhoff's HSP theorem states that every model of an algebra A is the homomorphic image...
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  • specifically in the theory of Lie algebras, the Poincaré–Birkhoff–Witt theorem (or PBW theorem) is a result giving an explicit description of the universal...
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  • Zeilberger–Bressoud theorem (combinatorics) Birkhoff's representation theorem (lattice theory) Boolean prime ideal theorem (mathematical logic) Bourbaki–Witt theorem (order...
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  • Thumbnail for Frucht's theorem
    vertices, that every finite partial order is equivalent by Birkhoff's representation theorem to a finite distributive lattice, it follows that every finite...
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  • ones that hold in all lattices of sets in the above sense. Birkhoff's representation theorem for distributive lattices states that every finite distributive...
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  • Birkhoff's representation theorem Birkhoff's HSP theorem Birkhoff's theorem Birkhoff–Kakutani theorem Pierce–Birkhoff conjecture Pierce–Birkhoff ring...
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  • Thumbnail for Duality theory for distributive lattices
    bounded distributive lattices. Representation theorem Birkhoff's representation theorem Stone's representation theorem for Boolean algebras Stone duality...
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  • In mathematics, the Birkhoff–Grothendieck theorem classifies holomorphic vector bundles over the complex projective line. In particular every holomorphic...
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  • distributive lattice generated by X . {\displaystyle X.} Birkhoff's representation theorem for distributive lattices states that every finite distributive...
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  • graph of a distributive lattice that may be obtained via Birkhoff's representation theorem from a zigzag poset, a partially ordered set defined by an...
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  • exists a representation of the desired form. Atiyah–Bott fixed-point theorem Banach fixed-point theorem Bekić's theorem Borel fixed-point theorem Bourbaki–Witt...
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  • (with continuous mappings). Another case of Stone duality is Birkhoff's representation theorem stating a duality between finite partial orders and finite...
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  • Thumbnail for Euclidean geometry
    and to make clear the ramifications of the parallel postulate. Birkhoff's axioms: Birkhoff proposed four postulates for Euclidean geometry that can be confirmed...
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  • Thumbnail for Dedekind–MacNeille completion
    to x. The result is a distributive lattice and is used in Birkhoff's representation theorem. However, it may have many more elements than are needed to...
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  • described in the 1970s by John Horton Conway and Donald Knuth. By Birkhoff's representation theorem, this lattice can be represented as the lower sets of an underlying...
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  • is isomorphic to a lattice of sets, ordered by inclusion (Birkhoff's representation theorem). A semilattice is partially ordered set with only one of...
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  • Thumbnail for Partially ordered set
    class of partial orders, called distributive lattices; see Birkhoff's representation theorem. Sequence A001035 in OEIS gives the number of partial orders...
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  • Thumbnail for Dedekind number
    operations, forms a distributive lattice, the lattice given by Birkhoff's representation theorem from the partially ordered set of subsets of the n {\displaystyle...
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  • Stone duality, connecting sober spaces and spatial locales. Birkhoff's representation theorem relating distributive lattices and partial orders Pontryagin...
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  • Thumbnail for Fence (mathematics)
    lattice with this many elements, generated from a fence via Birkhoff's representation theorem, has as its graph the Fibonacci cube. A partially ordered...
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  • Knowledge space (category Knowledge representation)
    and set intersection. The name "quasi-ordinal" arises from Birkhoff's representation theorem, which explains that distributive lattices uniquely correspond...
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  • and finite topologies can be interpreted as a version of Birkhoff's representation theorem, an equivalence between finite distributive lattices (the...
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  • Thumbnail for Topological group
    {\displaystyle r>0} , are pre-compact. The Birkhoff–Kakutani theorem (named after mathematicians Garrett Birkhoff and Shizuo Kakutani) states that the following...
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  • Thumbnail for Antimatroid
    antimatroid forming the linear extensions of the partial order. By Birkhoff's representation theorem for distributive lattices, the feasible sets in a poset antimatroid...
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  • Thumbnail for Lie algebra representation
    In the mathematical field of representation theory, a Lie algebra representation or representation of a Lie algebra is a way of writing a Lie algebra...
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