English

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.

Keywords

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

R2 v1 2026-06-21T22:51:32.402Z