  It is known after the works of Mahler, Kleinbock, Margulis, Sprind\v{z}uk and
others that very well approximated numbers on a manifold form a zero measure
set, assuming non-degeneracy conditions. These non-degeneracy conditions are,
in many applications, difficult to check. We propose here a setting in which
these are automatic. Rather than functions, we consider correspondences which
have a better behaviour.
