partially ordered set

Noun

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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**.

- A
**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**T_{M}.

- In sections 7-10 we shall consider random fields over some subsets T of the
**2000**, David Arnold,*Abelian Groups and Representations of Finite*, Springer, page 45 ↗,**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]).

- The invention of a derivative of a finite

- (
*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 0.004