complete lattice is a partially ordered set in which all subsets have both a supremum (join) and an infimum (meet). A conditionally complete lattice satisfies...

applied to lattices as follows: A continuous lattice is a complete lattice that is continuous as a poset. An algebraic lattice is a complete lattice that is...

familiar example is the completeness of the real numbers. A special use of the term refers to complete partial orders or complete lattices. However, many other...

lattice theory, the Knaster–Tarski theorem, named after Bronisław Knaster and Alfred Tarski, states the following: Let (L, ≤) be a complete lattice and...

in domain theory. As an important special case, an algebraic lattice is a complete lattice L where every element x of L is the supremum of the compact...

elements of a complete lattice, and let F be the set of choice functions f choosing for each index j of J some index f(j) in K(j). A complete lattice is completely...

negative infinities to the real line to give the complete totally ordered set [−∞,∞], which is a complete lattice. Consider a sequence ( x n ) {\displaystyle...

κ, there is a free (or universal) κ-complete Boolean algebra generated by any given set. Complete lattice Complete Heyting algebra Stavi 1974. Johnstone...

meet of the empty set), it is also a complete lattice. Thus a complete semilattice turns out to be "a complete lattice possibly lacking a top". This definition...

but rather the topology generated by the union. Every complete lattice is also a bounded lattice, which is to say that it has a greatest and least element...

images, it has been expanded first to grayscale images, and then to complete lattices. The dilation operation usually uses a structuring element for probing...

<). Complete Boolean algebra. A Boolean algebra that is a complete lattice. Complete Heyting algebra. A Heyting algebra that is a complete lattice is called...

meet-semilattice is a lattice. A lattice in which every subset, not just every pair, possesses a meet and a join is a complete lattice. It is also possible...

semilattice" in some publications. Originally, Dana Scott demanded a complete lattice, and the Russian mathematician Yuri Yershov constructed the isomorphic...

compact. A totally ordered set (with its order topology) which is a complete lattice is compact. Examples are the closed intervals of real numbers, e.g...

minimal dcpo. Every finite poset is directed complete. All complete lattices are also directed complete. For any poset, the set of all non-empty filters...

Dedekind–MacNeille completion of a partially ordered set is the smallest complete lattice that contains it. It is named after Holbrook Mann MacNeille whose 1937...

I} is a filter (which is then also prime, in the dual sense). For a complete lattice the further notion of a completely prime ideal is meaningful. It is...

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

two-point lattices { 0 , 1 } {\displaystyle \{0,1\}} .: p.56, Theorem 44  A continuous complete lattice is often called a continuous lattice. For a topological...

decomposing them into subsets called concepts, and placing them in a complete lattice. In some systems of axiomatic set theory, relations are extended to...

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

free lattice is the free object corresponding to a lattice. As free objects, they have the universal property. Because the concept of a lattice can be...

that data tables can be transformed into algebraic structures called complete lattices, and that these can be utilized for data visualization and interpretation...

distributive lattices. Every Boolean algebra is a Heyting algebra when a → b is defined as ¬a ∨ b, as is every complete distributive lattice satisfying...

Post's lattice denotes the lattice of all clones on a two-element set {0, 1}, ordered by inclusion. It is named for Emil Post, who published a complete description...

Ehresmann's approach involved using a category whose objects were complete lattices which satisfied a distributive law and whose morphisms were maps which...

the protein folding problem is NP-complete. Different versions of lattice proteins may adopt different types of lattice (typically square and triangular...

C is a meet-complete sublattice of P(S). Even for non-topological closure operators, C can be seen as having the structure of a lattice. (The join of...

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...