the lattice operations can be given by set union and intersection. Indeed, these lattices of sets describe the scenery completely: every distributive lattice...
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theory, a completely distributive lattice is a complete lattice in which arbitrary joins distribute over arbitrary meets. Formally, a complete lattice L is...
5 KB (649 words) - 22:30, 2 June 2024
are given in the article distributivity (order theory). This also includes the notion of a completely distributive lattice. In the presence of an ordering...
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Continuous posets, prime spectra of completely distributive complete lattices, and Hausdorff compactifications. Continuous Lattices. Vol. 871. pp. 159–208. doi:10...
40 KB (5,663 words) - 17:53, 6 June 2024
concept of distributivity, applied to the formation of suprema and infima. Most of these apply to partially ordered sets that are at least lattices, but the...
8 KB (1,065 words) - 09:40, 6 November 2023
case the complete lattice X is constructively completely distributive. See also the articles on complete distributivity and distributivity (order theory)...
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(order theory) Dense order Distributivity (order theory) modular lattice distributive lattice completely distributive lattice Ascending chain condition...
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that are not already complete lattices. Completely distributive lattice. A complete lattice is completely distributive if arbitrary joins distribute over...
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lattice: a lattice in which arbitrary meet and joins exist. Bounded lattice: a lattice with a greatest element and least element. Distributive lattice: a lattice...
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Heyting algebra (redirect from Brouwer lattice)
nonempty distributive lattice, in particular every nonempty finite chain, is automatically complete and completely distributive, and hence a Heyting algebra...
44 KB (6,243 words) - 20:32, 22 July 2024
Ideal (order theory) (redirect from Ideal (lattice theory))
is no proper filter that is a strict superset. When a poset is a distributive lattice, maximal ideals and filters are necessarily prime, while the converse...
13 KB (1,766 words) - 09:56, 30 January 2024
In mathematics, the notions of an absolutely monotonic function and a completely monotonic function are two very closely related concepts. Both imply very...
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Stone duality (section The lattice of open sets)
DLat01 of bounded distributive lattices. Hence, DLat01 is dual to CohSp—one obtains Stone's representation theorem for distributive lattices. When restricting...
15 KB (2,289 words) - 16:40, 23 August 2024
Algebra over a field (redirect from Distributive algebra)
space is commutative, left distributivity and right distributivity are equivalent, and, in this case, only one distributivity requires a proof. In general...
22 KB (2,935 words) - 02:08, 13 August 2024
analysis (second ed.). Grätzer, George (1971). Lattice theory: first concepts and distributive lattices. ISBN 0-7167-0442-0. Pemberton, Malcolm; Rau, Nicholas...
19 KB (2,467 words) - 04:06, 27 August 2024
later being extended to grayscale images, and subsequently to complete lattices. The erosion operation usually uses a structuring element for probing and...
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lattice basis, it suffices to define a Boolean algebra as a distributive lattice satisfying x∧¬x = 0 and x∨¬x = 1, called a complemented distributive...
65 KB (8,235 words) - 09:01, 4 February 2024
"logical" structures such as semilattices, distributive lattices, complete and completely distributive lattices, Boolean algebras, complete atomic Boolean...
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prefix oct(o)-, as in the ordinal adjective octaval or octavary, the distributive adjective is octonary. The adjective octuple (Latin octu-plus) may also...
74 KB (7,953 words) - 19:05, 4 September 2024
covering relation of a Tamari lattice is the skeleton of an associahedron. The covering relation of any finite distributive lattice forms a median graph. On...
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both left and right semimedial Left distributive If it satisfies the identity x • yz ≡ xy • xz Right distributive If it satisfies the identity yz • x...
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fixed N The Boolean lattice of finite subsets of a set ordered by inclusion (number of elements of the subset) Any distributive lattice of finite lower sets...
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a module is an additive abelian group, and scalar multiplication is distributive over the operations of addition between elements of the ring or module...
21 KB (2,941 words) - 13:38, 7 August 2024
axiomatization of Boolean algebra, such as the axioms for a complemented distributive lattice, a sufficient condition for an algebraic structure of this kind to...
75 KB (9,506 words) - 17:24, 21 June 2024
and the given topology on X coincide. The order topology makes X into a completely normal Hausdorff space. The standard topologies on R, Q, Z, and N are...
15 KB (2,106 words) - 09:57, 1 September 2024
multiplication is given by concatenating such symbols, imposing the distributive law under addition, and requiring that scalar multiplication commute...
87 KB (11,494 words) - 16:23, 2 August 2024
John von Neumann (category Lattice theorists)
Consequently, the distributive law of classical logic must be replaced with a weaker condition. Instead of a distributive lattice, propositions about...
205 KB (23,338 words) - 06:15, 5 September 2024
theorem stating a duality between finite partial orders and finite distributive lattices. In pointless topology the category of spatial locales is known...
14 KB (1,988 words) - 19:46, 11 July 2024
and that parentheses may be omitted in both cases. Multiplication is distributive over addition, which means that a ( b + c ) = a b + a c {\displaystyle...
61 KB (8,208 words) - 21:57, 25 August 2024
{\displaystyle S,} ordered by inclusion, is a bounded lattice, and hence together with the distributive and complement laws above, show that it is a Boolean...
171 KB (29,870 words) - 21:12, 7 August 2024