About: Inverse function theorem

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Theorem that, if a function is continuously differentiable with nonzero Jacobian determinant at a given point, then it is locally invertible near that point

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  • matematikai állítás (hu)
  • mathematischer Satz (de)
  • theorem that, if a function is continuously differentiable with nonzero Jacobian determinant at a given point, then it is locally invertible near that point (en)
  • Condiciones suficientes para la invertibilidad local de una función (es)
  • proporciona as condicións suficientes para que unha aplicación sexa invertíbel localmente no contorno dun punto p en termos da súa derivada no punto (gl)
  • la teoremo, ke kontinue derivebla funkcio estas loke inversigebla ĉirkaŭ punkto ĉe kiu la Jacobi-determinanto de la funkcio estas nenula (eo)
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  • Let denote an open ball of radius r in with center 0 and a map with a constant such that : for all in . Then for on , we have : in particular, f is injective. If, moreover, , then :. More generally, the statement remains true if is replaced by a Banach space. Also, the first part of the lemma is true for any normed space. (en)
  • Let be a map between open subsets of or more generally of manifolds. Assume is continuously differentiable . If is injective on a closed subset and if the Jacobian matrix of is invertible at each point of , then is injective on a neighborhood of and is continuously differentiable . (en)
  • If is a closed subset of a topological manifold and , some topological space, is a local homeomorphism that is injective on , then is injective on some neighborhood of . (en)
  • Let be open subsets such that and a holomorphic map whose Jacobian matrix in variables is invertible at . Then is injective in some neighborhood of and the inverse is holomorphic. (en)
  • If is an injective holomorphic map between open subsets of , then is holomorphic. (en)
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  • Proposition (en)
  • Theorem (en)
  • Lemma (en)
  • Inverse function theorem (en)
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  • Inverse function theorem (en)
  • Teorema de la funció inversa (ca)
  • Věta o inverzní funkci (cs)
  • Théorème d'inversion locale (fr)
  • Satz von der Umkehrabbildung (de)
  • Teorema de la función inversa (es)
  • Teorema della funzione inversa (it)
  • 逆函数定理 (ja)
  • 역함수 정리 (ko)
  • Teorema da função inversa (pt)
  • Теорема об обратной функции (ru)
  • Теорема про обернену функцію (uk)
  • Inversa funktionssatsen (sv)
  • 反函数定理 (zh)
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