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arXiv · 1212.2066

The Implicit and the Inverse Function theorems: easy proofs

Oswaldo Rio Branco de Oliveira
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Abstract

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.

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Oswaldo Rio Branco de Oliveira. 2012-12-10. The Implicit and the Inverse Function theorems: easy proofs. https://doi.org/10.14321/realanalexch.39.1.0207

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