Difference between revisions of "Borel isomorphism"
From Encyclopedia of Mathematics
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| − | A one-to-one mapping | + | A one-to-one mapping $f$ of a space $X$ into a space $Y$ such that both $f$ and $f^{-1}$ transform Borel sets into Borel sets (cf. [[Borel set|Borel set]]). In the class of Borel subsets of complete separable metric spaces, sets of the same cardinality are Borel isomorphic. |
Latest revision as of 14:02, 21 June 2014
$B$-isomorphism
A one-to-one mapping $f$ of a space $X$ into a space $Y$ such that both $f$ and $f^{-1}$ transform Borel sets into Borel sets (cf. Borel set). In the class of Borel subsets of complete separable metric spaces, sets of the same cardinality are Borel isomorphic.
How to Cite This Entry:
Borel isomorphism. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Borel_isomorphism&oldid=16905
Borel isomorphism. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Borel_isomorphism&oldid=16905
This article was adapted from an original article by A.G. El'kin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article