Isolated zeros of Lipschitzian metrically regular ℝn-functions

Abstract

Given a metrically regular locally Lipschitzian function sending ${ℝn}$ into ${ℝm}$,the structure of the preimages will be studied. In particular, for the case of m =n, it will be shown that all preimages are locally finite sets provided that the Lipschitzian function in question is directionally differentiable. Some consequences of this fact will be discussed.