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arXiv · 1812.03561

An Inverse Function Theorem Converse

Jimmie D. Lawson
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Abstract

We establish the following converse of the well-known inverse function theorem. Let $g:U\to V$ and $f:V\to U$ be inverse homeomorphisms between open subsets of Banach spaces. If $g$ is differentiable of class $C^p$ and $f$ if locally Lipschitz, then the Fr\'echet derivative of $g$ at each point of $U$ is invertible and $f$ must be differentiable of class $C^p$.

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Jimmie D. Lawson. 2018-12-09. An Inverse Function Theorem Converse. https://arxiv.org/abs/1812.03561

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