  We study the global inversion of a continuous nonsmooth mapping $f:
\mathbb{R}^n \rightarrow \mathbb{R}^n$, which may be non-locally Lipschitz. To
this end, we use the notion of pseudo-Jacobian map associated to f, introduced
by Jeyakumar and Luc, and we consider a related index of regularity for f. We
obtain a characterization of global inversion in terms of its index of
regularity. Furthermore, we prove that the Hadamard integral condition has a
natural counterpart in this setting, providing a sufficient condition for
global invertibility.
