# Borel isomorphism

From Encyclopedia of Mathematics

*$B$-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://www.encyclopediaofmath.org/index.php?title=Borel_isomorphism&oldid=32288

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