partially ordered
adjective Date: 1941 having some or all elements connected by a relation that is reflexive, transitive, and antisymmetric

New Collegiate Dictionary. 2001.

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  • partially ordered — adjective Of a set, having a specified partial order; often construed with by …   Wiktionary

  • partially ordered — adjective : having some or all mathematical elements connected by a relation that is reflexive, transitive, and antisymmetric …   Useful english dictionary

  • Partially ordered set — The Hasse diagram of the set of all subsets of a three element set {x, y, z}, ordered by inclusion. In mathematics, especially order theory, a partially ordered set (or poset) formalizes and generalizes the intuitive concept of an ordering,… …   Wikipedia

  • Partially-ordered group — In abstract algebra, a partially ordered group is a group (G,+) equipped with a partial order ≤ that is translation invariant; in other words, ≤ has the property that, for all a, b, and g in G, if a ≤ b then a+g ≤ b+g and g+a ≤ g+b. An element x… …   Wikipedia

  • partially ordered set — Math. a set in which a relation as less than or equal to holds for some pairs of elements of the set, but not for all. Cf. totally ordered set, well ordered set. [1970 75] * * * …   Universalium

  • partially ordered set — Math. a set in which a relation as less than or equal to holds for some pairs of elements of the set, but not for all. Cf. totally ordered set, well ordered set. [1970 75] …   Useful english dictionary

  • partially ordered set — noun a) A set having a specified partial order. b) Said set together with said partial order; the ordered pair of said set and said partial order. Syn: poset …   Wiktionary

  • Ordered group — In abstract algebra, an ordered group is a group (G,+) equipped with a partial order ≤ which is translation invariant ; in other words, ≤ has the property that, for all a , b , and g in G , if a ≤ b then a+g ≤ b+g and g+a ≤ g+b . Note that… …   Wikipedia

  • Ordered vector space — A point x in R2 and the set of all y such that x≤y (in red). The order here is x≤y if and only if x1 ≤ y1 and x2 ≤ y2. In mathematics an ordered vector space or partially ordered vector space is a vector space equi …   Wikipedia

  • Ordered set — In order theory in mathematics, a set with a binary relation R on its elements that is reflexive (for all a in the set, aRa), antisymmetric (if aRb and bRa, then a = b) and transitive (if aRb and bRc, then aRc) is described as a… …   Wikipedia

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