partially ordered set en · NOUN
Meanings
- (broadly) A set that has a given, elsewhere specified partial order.
-
(formal) The ordered pair comprising a set and its partial order.
1959 [D. Van Nostrand], Edward James McShane, Truman Arthur Botts, Real Analysis, 2005, Dover, page 28, A partially ordered set means a pair (P,≻) consisting of a set P and a partial order ≻ in P. As usual, when the meaning is clear, we may suppress the notation of "≻" and speak of the partially ordered set P. The ordered fields defined earlier are easily seen to be examples of partially ordered sets.
The invention of a derivative of a finite partially ordered set by Nazarova and Roiter in the late 1960s or early 1970s was a seminal event in the subject of representations of finite partially ordered sets (see [Simson 92]).
2000, David Arnold, Abelian Groups and Representations of Finite Partially Ordered Sets, Springer, page 45:In sections 7-10 we shall consider random fields over some subsets T of the partially ordered set T_M.
1994, I. V. Evstigneev, P. E. Greenwood, Markov Fields over Countable Partially Ordered Sets: Extrema and Splitting, American Mathematical Society, page 35:
Forms
| Spelling | Features | Labels | Source |
|---|---|---|---|
| partially ordered sets | Number=Plur | lexicographic |
Hypernyms
Hyponyms
lattice · distributive lattice · totally ordered set · complete lattice · Boolean lattice
Relateds
partial order · complete partial order
Synonyms
poset (set on which a partial order is defined) · partially ordered set · poset (ordered pair of set and partial order) · ground set (set on which a partial order is defined)
Translations (11)
fi osittain järjestetty joukko (set having a specified partial order) · sv partiellt ordnad mängd (set having a specified partial order) · pl częściowy porządek (set having a specified partial order) · de partiell geordnete Menge (set having a specified partial order) · cs uspořádaná množina (set having a specified partial order) · es copo (set having a specified partial order) · ar مَجْمُوعَةٌ مُرَتَّبَةٌ جُزْئِيًّا (set having a specified partial order) · ja 半順序集合 (set having a specified partial order) · ar فِئَةٌ مُرَتَّبَةٌ جُزْئِيًّا (set having a specified partial order) · es poset (set having a specified partial order) · es conjunto parcialmente ordenado (set having a specified partial order)