Borel isomorphism

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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.

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Borel isomorphism. Encyclopedia of Mathematics. URL:
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