the lattice operations can be given by set union and intersection. Indeed, these lattices of sets describe the scenery completely: every distributive lattice...

theory, a completely distributive lattice is a complete lattice in which arbitrary joins distribute over arbitrary meets. Formally, a complete lattice L is...

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...

are given in the article distributivity (order theory). This also includes the notion of a completely distributive lattice. In the presence of an ordering...

Continuous posets, prime spectra of completely distributive complete lattices, and Hausdorff compactifications. Continuous Lattices. Vol. 871. pp. 159–208. doi:10...

(order theory) Dense order Distributivity (order theory) Modular lattice Distributive lattice Completely distributive lattice Ascending chain condition...

that are not already complete lattices. Completely distributive lattice. A complete lattice is completely distributive if arbitrary joins distribute over...

case the complete lattice X is constructively completely distributive. See also the articles on complete distributivity and distributivity (order 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...

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...

DLat01 of bounded distributive lattices. Hence, DLat01 is dual to CohSp—one obtains Stone's representation theorem for distributive lattices. When restricting...

nonempty distributive lattice, in particular every nonempty finite chain, is automatically complete and completely distributive, and hence a Heyting algebra...

"logical" structures such as semilattices, distributive lattices, complete and completely distributive lattices, Boolean algebras, complete atomic Boolean...

later being extended to grayscale images, and subsequently to complete lattices. The erosion operation usually uses a structuring element for probing and...

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...

analysis (second ed.). Grätzer, George (1971). Lattice theory: first concepts and distributive lattices. W. H. Freeman. ISBN 0-7167-0442-0. Pemberton,...

space is commutative, left distributivity and right distributivity are equivalent, and, in this case, only one distributivity requires a proof. In general...

In mathematics, the notions of an absolutely monotonic function and a completely monotonic function are two very closely related concepts. Both imply very...

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...

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...

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...

multiplication is given by concatenating such symbols, imposing the distributive law under addition, and requiring that scalar multiplication commute...

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...

[ a , x , b ] {\displaystyle [a,x,b]} . The system of open intervals completely defines the cyclic order and can be used as an alternate definition of...

a module is an additive abelian group, and scalar multiplication is distributive over the operations of addition between elements of the ring or module...

Consequently, the distributive law of classical logic must be replaced with a weaker condition. Instead of a distributive lattice, propositions about...

axiomatization of Boolean algebra, such as the axioms for a complemented distributive lattice, a sufficient condition for an algebraic structure of this kind to...

convention in set theory given above. The axioms are: The axioms for a distributive lattice (see above) ∀a a∧¬a = 0, ∀a a∨¬a = 1 (properties of negation) Some...

theorem stating a duality between finite partial orders and finite distributive lattices. In pointless topology the category of spatial locales is known...

{\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...