[Merged by Bors] - feat(analysis/calculus/inverse): a function with onto strict derivative is locally onto #6229
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| /-- A surjective continuous linear map admits a (possibly nonlinear) controlled right inverse. | ||
| In general, it is not possible to ensure that such a right inverse is linear. -/ |
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Could you please add "between Banach spaces"?
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src/analysis/calculus/inverse.lean
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| @@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE. | |||
| Authors: Yury Kudryashov, Heather Macbeth. | |||
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| Authors: Yury Kudryashov, Heather Macbeth. | |
| Authors: Yury Kudryashov, Heather Macbeth, Sébastien Gouëzel. |
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Thanks! |
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…ve is locally onto (#6229) Removes a useless assumption in `map_nhds_eq_of_complemented` (no need to have a completemented subspace). The proof of the local inverse theorem breaks into two parts, local injectivity and local surjectivity. We refactor the local surjectivity part, assuming in the proof only that the derivative is onto. The result is stronger, but the proof is less streamlined since there is no contracting map any more: we give a naive proof from first principles instead of reducing to the fixed point theorem for contracting maps.
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…ve is locally onto (#6229) Removes a useless assumption in `map_nhds_eq_of_complemented` (no need to have a completemented subspace). The proof of the local inverse theorem breaks into two parts, local injectivity and local surjectivity. We refactor the local surjectivity part, assuming in the proof only that the derivative is onto. The result is stronger, but the proof is less streamlined since there is no contracting map any more: we give a naive proof from first principles instead of reducing to the fixed point theorem for contracting maps.
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Removes a useless assumption in
map_nhds_eq_of_complemented(no need to have a completemented subspace).The proof of the local inverse theorem breaks into two parts, local injectivity and local surjectivity. We refactor the local surjectivity part, assuming in the proof only that the derivative is onto. The result is stronger, but the proof is less streamlined since there is no contracting map any more: we give a naive proof from first principles instead of reducing to the fixed point theorem for contracting maps.