An Inverse Function Theorem Converse
| Autor: | Lawson, Jimmie D. |
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| Rok vydání: | 2018 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $C^p$. Comment: 8 pages |
| Databáze: | arXiv |
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