partially ordered
Adjective
Meaning
partially ordered (not comparable)
(set theory, order theory, of a set) Equipped with a partial order; when the partial order is specified, often construed with by.
Examples
A heap is not a sorted structure and can be regarded as partially ordered.
An abstract polyhedron is a certain kind of partially ordered set (poset) of elements, such that adjacencies, or connections, between elements of the set correspond to adjacencies between elements (faces, edges, etc.) of a polyhedron.
A pair of adjoint functors between two partially ordered sets is called a Galois connection (or, if it is contravariant, an antitone Galois connection).
Definition A partially ordered set (poset) P is said to satisfy the ascending chain condition (ACC) if every strictly ascending sequence of elements eventually terminates.
Empty chain as boundary case In the formulation of Zorn's lemma above, the partially ordered set P is not explicitly required to be non-empty.
Complete lattices must not be confused with complete partial orders (cpos), which constitute a strictly more general class of partially ordered sets.