THE IMPLICIT AND THE INVERSE FUNCTION THEOREMS: EASY PROOFS

By Oswaldo Rio Branco de Oliveira. 2012

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This article presents simple and easy proofs of the Implicit Function Theorem and the Inverse Function Theorem, in this order, both of them on a finite-dimensional Euclidean space, that employ only the Intermediate Value Theorem and the Mean-Value Theorem. These proofs avoid compactness arguments, the contraction principle, and fixed-point theorems. Mathematics Subject Classification: 26B10, 26B12, 97I40, 97I60

Subfields: Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/c4daf50d56267a3e3906fbd57cd4acce249d41ca