In mathematics, the phrase complete partial order is variously used to refer to at least three similar, but distinct, classes of partially ordered sets...

especially order theory, a partial order on a set is an arrangement such that, for certain pairs of elements, one precedes the other. The word partial is used...

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...

(infima) exist. Complete partial order. A complete partial order, or cpo, is a directed complete partial order (q.v.) with least element. Complete relation....

mathematics, a total order or linear order is a partial order in which any two elements are comparable. That is, a total order is a binary relation ≤...

axiom, this preorder is even a partial order (called the specialization order). On the other hand, for T1 spaces the order becomes trivial and is of little...

Partial-order planning is an approach to automated planning that maintains a partial ordering between actions and only commits ordering between actions...

Ordinal number Well-quasi-ordering Semilattice Lattice (Directed) complete partial order, (d)cpo Bounded complete Complete lattice Knaster–Tarski theorem...

bound also have a least upper bound. Such a partial order can also be called consistently or coherently complete (Visser 2004, p. 182), since any upper bound...

ordered set Complete partial order Permutation, the act of arranging all the members of a set into some sequence or order Ranking Stochastic ordering of random...

see completeness). Another usage of "complete meet-semilattice" refers to a meet-semilattice that is bounded complete and a complete partial order. This...

In order-theoretic mathematics, a series-parallel partial order is a partially ordered set built up from smaller series-parallel partial orders by two...

Pontifical Order of Pius IX, female variant of a class in one of the orders of knighthood of the Holy See Directed complete partial order, in mathematics...

a cyclic order if it is cyclic, asymmetric, transitive, and connected. Dropping the "connected" requirement results in a partial cyclic order. A set with...

and definitions such as "ideal", "order ideal", "Frink ideal", or "partial order ideal" mean one another. An important special case of an ideal is constituted...

United States Postal Service Complete partial order, a term used in mathematical order theory Compulsory purchase order, a legal function in the UK and...

mathematics, a partial cyclic order is a ternary relation that generalizes a cyclic order in the same way that a partial order generalizes a linear order. Over...

set is also a partial order in which every two distinct elements are incomparable. It is also the only relation that is both a partial order and an equivalence...

In mathematics, a first-order partial differential equation is a partial differential equation that involves the first derivatives of an unknown function...

needed to cover all elements. This number is called the width of the partial order. The theorem is named for the mathematician Robert P. Dilworth, who...

_{Q}f(B)} . A subset of a directed complete partial order is closed with respect to the Scott topology induced by the partial order if and only if it is a lower...

order theory, a branch of mathematics, a linear extension of a partial order is a total order (or linear order) that is compatible with the partial order...

)} , the set of natural numbers with standard ordering, is a well partial order (in fact, a well-order). However, ( Z , ≤ ) {\displaystyle (\mathbb {Z}...

mathematical fields of order and domain theory, a Scott domain is an algebraic, bounded-complete and directed-complete partial order (dcpo). They are named...

value Polymorphism Calculus of constructions Domain theory Directed complete partial order Knaster–Tarski theorem Cartesian closed category Yoneda lemma Graph...

makes the specialization preorder a directed complete partial order. Every continuous directed complete poset equipped with the Scott topology is sober...

define the height of a partial order to be the maximum cardinality of a chain. Mirsky's theorem states that in any partial order of finite height, the...

New Friend". Antichain – Subset of incomparable elements Chain-complete partial order – a partially ordered set in which every chain has a least upper...

are seen as complete lattices, complete join-semilattices, complete meet-semilattices, or as join-complete or meet-complete lattices. "Partial lattice" is...

ordered sets (or posets), orderings in which some pairs are comparable and others might not be Preorders, a generalization of partial orders allowing ties...