# partially ordered set

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## partially ordered set

[′pär·shə·lē ¦ōr·dərd ′set]
(mathematics)
A set on which a partial order is defined. Also known as poset.

## partially ordered set

References in periodicals archive ?
Lopez, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22 (2005), 223-239.
Let (X, [less than or equal to]) be a partially ordered set and d be a metric on X such that (X, d) is complete.
However all the vertices are real and it is a partially ordered set.
That is, there is no order of succession implied by the space as in the partially ordered sets and grammars.
An ordered pair <S, R> where S is a set, and R is a relation from S to S, is a partially ordered set, if
7] Let (X, [less than or equal to]) be a partially ordered set and let there exist a metric d in X which makes (X, d) into a complete metric space.
Hence, (R, [less than or equal to]) is a partially ordered set.
Let (P, [less than or equal to]) be a finite partially ordered set (poset for short) and x, y [member of] P.
Then (G; [less than or equal to]) is a partially ordered set and 0 is its smallest element.
be a partially ordered set and f: X [right arrow] X and g: X [right arrow] X.
Let X be a partially ordered set and F: X x X [right arrow] CB(X) a mapping.

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