THE NECESSARV AND SUFFICIENT CONDITIONS FOR LIPSCHITZ LOCAL HOMEOMORPHISM |
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Affiliation: | Department of Mathematics, Lanzhou Univdisity Lanzhou 730000, Gansu, China. |
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Abstract: | 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. |
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