Local topological equivalence of nonsmooth functions in Hilbert spaces

In this paper we investigate the relation between nonsmooth functions with domain in a Hilbert space and their local approximations. We consider Lipschitz functions and define an approximation model with directional derivatives. The qualitative behaviour of the approximation is studied by means of the concept of topological equivalence. Using this concept we establish the existence of a local coordinate transformation between the original function and the local approximation.