poset

poset
noun /pôset/lang=sh

42. Definition. A poset (partially ordered set) (X, ≤) (usually written just X) is a set X together with a transitive, antisymmetric relation ≤ on X.

43. Definition. A linearly ordered set or chain is a poset (X, ≤), such that ∀a, b ∈ X, either a ≤ b or b ≤ a or a = b.


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  • Poset topology — In mathematics, the poset topology associated with a partially ordered set S (or poset for short) is the Alexandrov topology (open sets are upper sets) on the poset of finite chains of S, ordered by inclusion. Let V be a set of vertices. An… …   Wikipedia

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  • Graded poset — In mathematics, a graded poset, sometimes called a ranked poset (but see the article for an alternative meaning), is a partially ordered set (poset) P equipped with a rank function rho; from P to N compatible with the ordering (so rho;( x ) lt;… …   Wikipedia

  • Ranked poset — In mathematics, a ranked partially ordered set (or poset) may be either:* a graded poset, or * a poset that has the property that for every element x , all maximal chains among those with x as greatest element have the same finite length, or * a… …   Wikipedia

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