# Borel isomorphism

$B$-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.