  Let $\bf\Gamma$ be a Borel class, or a Wadge class of Borel sets, and $2\leq
d\leq\omega$ a cardinal. We study the Borel subsets of ${\mathbb R}^d$ that can
be made $\bf\Gamma$ by refining the Polish topology on the real line. These
sets are called potentially $\bf\Gamma$. We give a test to recognize
potentially $\bf\Gamma$ sets.
