partially ordered set
Noun
This text is extracted from the Wiktionary and it is available under the CC BY-SA 3.0 license | Terms and conditions | Privacy policy 0.003
Noun
partially ordered set
- (set theory, order theory, loosely) A set that has a given, elsewhere specified partial order.
- (set theory, order theory, formally) 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,\succ) consisting of a set P and a partial order \succ in P. As usual, when the meaning is clear, we may suppress the notation of "\succ" and speak of the partially ordered set P.
- The ordered fields defined earlier are easily seen to be examples of partially ordered sets.
- 1994, I. V. Evstigneev, P. E. Greenwood, Markov Fields over Countable Partially Ordered Sets: Extrema and Splitting, American Mathematical Society, page 35 ↗,
- In sections 7-10 we shall consider random fields over some subsets T of the partially ordered set TM.
- 2000, David Arnold, Abelian Groups and Representations of Finite Partially Ordered Sets, Springer, page 45 ↗,
- 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]).
- 1959 [D. Van Nostrand], Edward James McShane, Truman Arthur Botts, Real Analysis, 2005, Dover, page 28 ↗,
- (set on which a partial order is defined) ground set, poset
- (ordered pair of set and partial order) poset
- See also Thesaurus:partially ordered set
This text is extracted from the Wiktionary and it is available under the CC BY-SA 3.0 license | Terms and conditions | Privacy policy 0.003