# Isolated zeros of Lipschitzian metrically regular ℝn-functions

Fusek, P (2001). Isolated zeros of Lipschitzian metrically regular ℝn-functions. Optimization, 49(5-6):425-446.

## 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.

## 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.

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