The Implicit and the Inverse Function theorems: easy proofs
Classical Analysis and ODEs
2022-02-16 v1
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.
Cite
@article{arxiv.1212.2066,
title = {The Implicit and the Inverse Function theorems: easy proofs},
author = {Oswaldo Rio Branco de Oliveira},
journal= {arXiv preprint arXiv:1212.2066},
year = {2022}
}
Comments
10 pages