Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Borel_equivalence_relation> ?p ?o. }
Showing items 1 to 12 of
12
with 100 items per page.
- Borel_equivalence_relation abstract "In mathematics, a Borel equivalence relation on a Polish space X is an equivalence relation on X that is a Borel subset of X × X(in the product topology).Given Borel equivalence relations E and F on Polish spaces X and Y respectively, one says that E is Borel reducible to F, in symbols E ≤B F, if and only if there is a Borel functionΘ : X → Ysuch that for all x,x' ∈ X, one hasxEx' ⇔ Θ(x)FΘ(x' ).Conceptually, if E is Borel reducible to F, then E is "not more complicated" than F, and the quotient space X/E has a lesser or equal "Borel cardinality" than Y/F, where"Borel cardinality" is like cardinality except for a definability restriction on the witnessing mapping.".
- Borel_equivalence_relation wikiPageID "2123692".
- Borel_equivalence_relation wikiPageRevisionID "605742821".
- Borel_equivalence_relation hasPhotoCollection Borel_equivalence_relation.
- Borel_equivalence_relation subject Category:Descriptive_set_theory.
- Borel_equivalence_relation comment "In mathematics, a Borel equivalence relation on a Polish space X is an equivalence relation on X that is a Borel subset of X × X(in the product topology).Given Borel equivalence relations E and F on Polish spaces X and Y respectively, one says that E is Borel reducible to F, in symbols E ≤B F, if and only if there is a Borel functionΘ : X → Ysuch that for all x,x' ∈ X, one hasxEx' ⇔ Θ(x)FΘ(x' ).Conceptually, if E is Borel reducible to F, then E is "not more complicated" than F, and the quotient space X/E has a lesser or equal "Borel cardinality" than Y/F, where"Borel cardinality" is like cardinality except for a definability restriction on the witnessing mapping.".
- Borel_equivalence_relation label "Borel equivalence relation".
- Borel_equivalence_relation sameAs m.06ntf0.
- Borel_equivalence_relation sameAs Q4944905.
- Borel_equivalence_relation sameAs Q4944905.
- Borel_equivalence_relation wasDerivedFrom Borel_equivalence_relation?oldid=605742821.
- Borel_equivalence_relation isPrimaryTopicOf Borel_equivalence_relation.