A proof of the inverse function theorem

The purpose of this note is to give a proof, hopefully new, of the inverse function theorem as an application of the local existence theorem for differential equations. If Ω  is an open subset of a Banach space E and T: Ω → E is of class C1, then T is locally bounded and satisfies a Lipschitz condit...

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Autores:
Restrepo Sierra, Guillermo
Tipo de recurso:
Article of journal
Fecha de publicación:
1971
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
spa
OAI Identifier:
oai:repositorio.unal.edu.co:unal/42195
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/42195
http://bdigital.unal.edu.co/32292/
Palabra clave:
function theorem
theorem
differential equations
Rights
openAccess
License
Atribución-NoComercial 4.0 Internacional
Description
Summary:The purpose of this note is to give a proof, hopefully new, of the inverse function theorem as an application of the local existence theorem for differential equations. If Ω  is an open subset of a Banach space E and T: Ω → E is of class C1, then T is locally bounded and satisfies a Lipschitz condition at every point.