THE NECESSARV AND SUFFICIENT CONDITIONS FOR LIPSCHITZ LOCAL HOMEOMORPHISM

For a locally Lipschitz map f:$R^{n}\rightarrow R^{n}$,the well known inverse functin theorem gives a sufficient condition for f to be a Lipschitz local homeomorphims at a point $x_{0}$,that is,$\partial f(x_{0}$ is invertible.In this paper,it is showed that this condition is not necessary and some necessary and sufficient conditions are given.