Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Duality_(order_theory)> ?p ?o }
Showing triples 1 to 67 of
67
with 100 triples per page.
- Duality_(order_theory) abstract "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 set 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 posets 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.The importance of this simple definition stems from the fact that every definition and theorem of order theory can readily be transferred to the dual order. Formally, this is captured by the Duality Principle for ordered sets: If a given statement is valid for all partially ordered sets, then its dual statement, obtained by inverting the direction of all order relations and by dualizing all order theoretic definitions involved, is also valid for all partially ordered sets.If a statement or definition is equivalent to its dual then it is said to be self-dual. Note that the consideration of dual orders is so fundamental that it often occurs implicitly when writing ≥ for the dual order of ≤ without giving any prior definition of this \"new\" symbol.".
- Duality_(order_theory) thumbnail Duale_Verbaende.svg?width=300.
- Duality_(order_theory) wikiPageID "600618".
- Duality_(order_theory) wikiPageLength "3409".
- Duality_(order_theory) wikiPageOutDegree "31".
- Duality_(order_theory) wikiPageRevisionID "695684315".
- Duality_(order_theory) wikiPageWikiLink Antisymmetric_relation.
- Duality_(order_theory) wikiPageWikiLink Boolean_algebra_(structure).
- Duality_(order_theory) wikiPageWikiLink Cambridge_University_Press.
- Duality_(order_theory) wikiPageWikiLink Category:Duality_theories.
- Duality_(order_theory) wikiPageWikiLink Category:Order_theory.
- Duality_(order_theory) wikiPageWikiLink Closure_operator.
- Duality_(order_theory) wikiPageWikiLink Complete_lattice.
- Duality_(order_theory) wikiPageWikiLink Distributive_lattice.
- Duality_(order_theory) wikiPageWikiLink Equivalence_relation.
- Duality_(order_theory) wikiPageWikiLink Filter_(mathematics).
- Duality_(order_theory) wikiPageWikiLink Greatest_element.
- Duality_(order_theory) wikiPageWikiLink Hasse_diagram.
- Duality_(order_theory) wikiPageWikiLink Ideal_(order_theory).
- Duality_(order_theory) wikiPageWikiLink If_and_only_if.
- Duality_(order_theory) wikiPageWikiLink Infimum_and_supremum.
- Duality_(order_theory) wikiPageWikiLink Inverse_relation.
- Duality_(order_theory) wikiPageWikiLink Lattice_(order).
- Duality_(order_theory) wikiPageWikiLink List_of_Boolean_algebra_topics.
- Duality_(order_theory) wikiPageWikiLink Mathematics.
- Duality_(order_theory) wikiPageWikiLink Maximal_element.
- Duality_(order_theory) wikiPageWikiLink Monotonic_function.
- Duality_(order_theory) wikiPageWikiLink Order_isomorphism.
- Duality_(order_theory) wikiPageWikiLink Order_theory.
- Duality_(order_theory) wikiPageWikiLink Partially_ordered_set.
- Duality_(order_theory) wikiPageWikiLink Transpose_graph.
- Duality_(order_theory) wikiPageWikiLink Upper_set.
- Duality_(order_theory) wikiPageWikiLink File:Duale_Verbaende.svg.
- Duality_(order_theory) wikiPageWikiLinkText "Dual".
- Duality_(order_theory) wikiPageWikiLinkText "Duality (order theory)".
- Duality_(order_theory) wikiPageWikiLinkText "Dually".
- Duality_(order_theory) wikiPageWikiLinkText "dual order structure".
- Duality_(order_theory) wikiPageWikiLinkText "dual".
- Duality_(order_theory) wikiPageWikiLinkText "dualisation".
- Duality_(order_theory) wikiPageWikiLinkText "duality (order theory)".
- Duality_(order_theory) wikiPageWikiLinkText "duality in order theory".
- Duality_(order_theory) wikiPageWikiLinkText "duality principle for order theory".
- Duality_(order_theory) wikiPageWikiLinkText "duality".
- Duality_(order_theory) wikiPageWikiLinkText "dualize".
- Duality_(order_theory) wikiPageWikiLinkText "dualized".
- Duality_(order_theory) wikiPageWikiLinkText "dualizing".
- Duality_(order_theory) wikiPageWikiLinkText "dually".
- Duality_(order_theory) wikiPageWikiLinkText "opposite poset".
- Duality_(order_theory) wikiPageWikiLinkText "order dual".
- Duality_(order_theory) wikiPageWikiLinkText "order-theoretic dual".
- Duality_(order_theory) wikiPageWikiLinkText "principle of duality".
- Duality_(order_theory) wikiPageWikiLinkText "self-dual".
- Duality_(order_theory) wikiPageUsesTemplate Template:Citation.
- Duality_(order_theory) wikiPageUsesTemplate Template:Reflist.
- Duality_(order_theory) subject Category:Duality_theories.
- Duality_(order_theory) subject Category:Order_theory.
- Duality_(order_theory) type Field.
- Duality_(order_theory) type Theory.
- Duality_(order_theory) comment "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 set 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.".
- Duality_(order_theory) label "Duality (order theory)".
- Duality_(order_theory) sameAs Q554403.
- Duality_(order_theory) sameAs m.02v74t.
- Duality_(order_theory) sameAs Подвійне_відношення_порядку.
- Duality_(order_theory) sameAs Q554403.
- Duality_(order_theory) wasDerivedFrom Duality_(order_theory)?oldid=695684315.
- Duality_(order_theory) depiction Duale_Verbaende.svg.
- Duality_(order_theory) isPrimaryTopicOf Duality_(order_theory).