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...

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 ≤...

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

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

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

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...

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...

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...

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...

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...

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

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

_{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...

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...

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...

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

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...

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

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

greatest for the natural order of the integers). Preorders are closely related to equivalence relations and (non-strict) partial orders. Both of these are...

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...

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

Antichain – Subset of incomparable elements Bourbaki–Witt theorem Chain-complete partial order – a partially ordered set in which every chain has a least upper...

Suppose ( L , ⊑ ) {\displaystyle (L,\sqsubseteq )} is a directed-complete partial order (dcpo) with a least element, and let f : L → L {\displaystyle f:L\to...

into two types: partial moles and complete moles, where the term 'mole' simply denotes a clump of growing tissue or a ‘growth'. A complete mole is caused...

linear) order is a partial order in which any two elements are comparable; that is, the order relation is connected. Similarly, a strict partial order that...

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

every pair, possesses a meet and a join is a complete lattice. It is also possible to define a partial lattice, in which not all pairs have a meet or...