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Specialization_(pre)order abstract "In the branch of mathematics known as topology, the specialization (or canonical) preorder is a natural preorder on the set of the points of a topological space. For most spaces that are considered in practice, namely for all those that satisfy the T0 separation axiom, this preorder is even a partial order (called the specialization order). On the other hand, for T1 spaces the order becomes trivial and is of little interest.The specialization order is often considered in applications in computer science, where T0 spaces occur in denotational semantics. The specialization order is also important for identifying suitable topologies on partially ordered sets, as it is done in order theory.".
Specialization_(pre)order wikiPageExternalLink ~marcello.
Specialization_(pre)order wikiPageExternalLink ENTCS-8.pdf.
Specialization_(pre)order wikiPageID "542347".
Specialization_(pre)order wikiPageLength "9611".
Specialization_(pre)order wikiPageOutDegree "67".
Specialization_(pre)order wikiPageRevisionID "682093940".
Specialization_(pre)order wikiPageWikiLink Adjoint_functors.
Specialization_(pre)order wikiPageWikiLink Alexandroff_topology.
Specialization_(pre)order wikiPageWikiLink Alexandrov_space.
Specialization_(pre)order wikiPageWikiLink Alexandrov_topology.
Specialization_(pre)order wikiPageWikiLink Algebraic_geometry.
Specialization_(pre)order wikiPageWikiLink Antisymmetric_relation.
Specialization_(pre)order wikiPageWikiLink Category:Order_theory.
Specialization_(pre)order wikiPageWikiLink Category:Topology.
Specialization_(pre)order wikiPageWikiLink Category_of_preordered_sets.
Specialization_(pre)order wikiPageWikiLink Category_of_topological_spaces.
Specialization_(pre)order wikiPageWikiLink Category_theory.
Specialization_(pre)order wikiPageWikiLink Closed_set.
Specialization_(pre)order wikiPageWikiLink Closure_(topology).
Specialization_(pre)order wikiPageWikiLink Commutative_ring.
Specialization_(pre)order wikiPageWikiLink Complete_partial_order.
Specialization_(pre)order wikiPageWikiLink Computer_science.
Specialization_(pre)order wikiPageWikiLink Consistency.
Specialization_(pre)order wikiPageWikiLink Consistent.
Specialization_(pre)order wikiPageWikiLink Continuity_(topology).
Specialization_(pre)order wikiPageWikiLink Continuous_function.
Specialization_(pre)order wikiPageWikiLink Denotational_semantics.
Specialization_(pre)order wikiPageWikiLink Directed_complete_partial_order.
Specialization_(pre)order wikiPageWikiLink Directed_set.
Specialization_(pre)order wikiPageWikiLink Domain_theory.
Specialization_(pre)order wikiPageWikiLink Empty_set.
Specialization_(pre)order wikiPageWikiLink Equivalence_relation.
Specialization_(pre)order wikiPageWikiLink Functor.
Specialization_(pre)order wikiPageWikiLink Generic_point.
Specialization_(pre)order wikiPageWikiLink Genus.
Specialization_(pre)order wikiPageWikiLink Hausdorff_space.
Specialization_(pre)order wikiPageWikiLink If_and_only_if.
Specialization_(pre)order wikiPageWikiLink Infimum_and_supremum.
Specialization_(pre)order wikiPageWikiLink Intersection_(set_theory).
Specialization_(pre)order wikiPageWikiLink Kolmogorov_space.
Specialization_(pre)order wikiPageWikiLink Left_adjoint.
Specialization_(pre)order wikiPageWikiLink Lower_set.
Specialization_(pre)order wikiPageWikiLink Mathematics.
Specialization_(pre)order wikiPageWikiLink Maximal_element.
Specialization_(pre)order wikiPageWikiLink Maximal_ideal.
Specialization_(pre)order wikiPageWikiLink Minimal_element.
Specialization_(pre)order wikiPageWikiLink Monotonic_function.
Specialization_(pre)order wikiPageWikiLink Non-empty.
Specialization_(pre)order wikiPageWikiLink Open_set.
Specialization_(pre)order wikiPageWikiLink Order_consistent.
Specialization_(pre)order wikiPageWikiLink Order_theory.
Specialization_(pre)order wikiPageWikiLink Partial_order.
Specialization_(pre)order wikiPageWikiLink Partially_ordered_set.
Specialization_(pre)order wikiPageWikiLink Preorder.
Specialization_(pre)order wikiPageWikiLink Prime_ideal.
Specialization_(pre)order wikiPageWikiLink Prime_spectrum.
Specialization_(pre)order wikiPageWikiLink R0_space.
Specialization_(pre)order wikiPageWikiLink Reflexive_relation.
Specialization_(pre)order wikiPageWikiLink Scott_continuity.
Specialization_(pre)order wikiPageWikiLink Scott_topology.
Specialization_(pre)order wikiPageWikiLink Separation_axiom.
Specialization_(pre)order wikiPageWikiLink Sierpinski_space.
Specialization_(pre)order wikiPageWikiLink Sierpiński_space.
Specialization_(pre)order wikiPageWikiLink Singleton_(mathematics).
Specialization_(pre)order wikiPageWikiLink Singleton_set.
Specialization_(pre)order wikiPageWikiLink Sober_space.
Specialization_(pre)order wikiPageWikiLink Species.
Specialization_(pre)order wikiPageWikiLink Spectrum_of_a_ring.
Specialization_(pre)order wikiPageWikiLink Supremum.
Specialization_(pre)order wikiPageWikiLink Symmetric_relation.
Specialization_(pre)order wikiPageWikiLink T0_space.
Specialization_(pre)order wikiPageWikiLink T1_space.
Specialization_(pre)order wikiPageWikiLink Topological_indistinguishability.
Specialization_(pre)order wikiPageWikiLink Topological_space.
Specialization_(pre)order wikiPageWikiLink Topologically_indistinguishable.
Specialization_(pre)order wikiPageWikiLink Topology.
Specialization_(pre)order wikiPageWikiLink Transitive_relation.
Specialization_(pre)order wikiPageWikiLink Upper_set.
Specialization_(pre)order wikiPageWikiLink Upper_topology.
Specialization_(pre)order wikiPageWikiLink Valuation_(algebra).
Specialization_(pre)order wikiPageWikiLink Valuation_theory.
Specialization_(pre)order wikiPageWikiLinkText "Specialization (pre)order".
Specialization_(pre)order wikiPageWikiLinkText "canonical preorder".
Specialization_(pre)order wikiPageWikiLinkText "specialization (pre)order".
Specialization_(pre)order wikiPageWikiLinkText "specialization preorder".
Specialization_(pre)order hasPhotoCollection Specialization_(pre)order.
Specialization_(pre)order wikiPageUsesTemplate Template:Reflist.
Specialization_(pre)order subject Category:Order_theory.
Specialization_(pre)order subject Category:Topology.
Specialization_(pre)order hypernym Preorder.
Specialization_(pre)order comment "In the branch of mathematics known as topology, the specialization (or canonical) preorder is a natural preorder on the set of the points of a topological space. For most spaces that are considered in practice, namely for all those that satisfy the T0 separation axiom, this preorder is even a partial order (called the specialization order).".
Specialization_(pre)order label "Specialization (pre)order".
Specialization_(pre)order sameAs (pre)orden_de_especialización.
Specialization_(pre)order sameAs m.02n9n0.
Specialization_(pre)order sameAs Q5569420.
Specialization_(pre)order sameAs Q5569420.
Specialization_(pre)order sameAs 特殊化预序.
Specialization_(pre)order wasDerivedFrom Specialization_(pre)order?oldid=682093940.
Specialization_(pre)order isPrimaryTopicOf Specialization_(pre)order.