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In his beautiful paper on the central set from 1981, Y.~Yom\-din makes use ofa Lipschitz Inverse Function Theorem that seemingly has been unproved untilnow. After a brief discussion of a natural and straightforward Lipschitzcounterpart of an implicit function theorem we finally provide a proof ofYomdin's version holds. Therefore, Yomdin's Generic Structure Theorem, whoseupdated version is also presented here, concerning the medial axis (centralset) of a subset of %definable or subanalytic in ${\Rz}^n$ is now flawless.

On Yomdin's version of a Lipschitz Implicit Function Theorem and the geometry of medial axes