Duality (order theory)
In the mathematical area of order theory, every partially ordered set P gives rise to a dual (or opposite) partially ordered set which is often denoted by Pop or Pd. This dual order Pop is defined to be the same set, but with the inverse order, i.e. x ≤ y holds in Pop if and only if y ≤ x holds in P. It is easy to see that this construction, which can be depicted by flipping the Hasse diagram for P upside down, will indeed yield a partially ordered set. In a broader sense, two partially ordered sets are also said to be duals if they are dually isomorphic, i.e. if one poset is order isomorphic to the dual of the other.
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Boolean algebra (structure)Boolean prime ideal theoremBound graphCharacterizations of the category of topological spacesClosure operatorCofinal (mathematics)Complete latticeComplete partial orderCompletely distributive latticeCompleteness (order theory)Cyclic groupDedekind–MacNeille completionDeviation of a posetDistributive latticeDistributivity (order theory)DivisorDual (category theory)Dual orderDualityDuality (mathematics)Duality principleErnst SchröderFilter (mathematics)Galois connectionGeometric latticeGlossary of order theoryGreatest element and least elementIdeal (order theory)Infimum and supremumInterior algebraInverse orderJoin and meetKnaster–Tarski theoremLattice (order)Least common multipleLimit-preserving function (order theory)List of Boolean algebra topicsList of dualitiesList of order theory topicsMaximal and minimal elements
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Duality (order theory)
In the mathematical area of order theory, every partially ordered set P gives rise to a dual (or opposite) partially ordered set which is often denoted by Pop or Pd. This dual order Pop is defined to be the same set, but with the inverse order, i.e. x ≤ y holds in Pop if and only if y ≤ x holds in P. It is easy to see that this construction, which can be depicted by flipping the Hasse diagram for P upside down, will indeed yield a partially ordered set. In a broader sense, two partially ordered sets are also said to be duals if they are dually isomorphic, i.e. if one poset is order isomorphic to the dual of the other.
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En el área matemática de la te ...... revia de este símbolo "nuevo".
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In the mathematical area of or ...... finition of this "new" symbol.
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Принцип двоїстості в частково ...... розуміють саме це твердження.
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En el área matemática de la te ...... ordenado es al dual del otro.
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In the mathematical area of or ...... phic to the dual of the other.
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Принцип двоїстості в частково ...... терміни залишаються без змін.
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Dualidad (teoría del orden)
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Duality (order theory)
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