The Implicit and the Inverse Function Theorems: Easy Proofs
Oswaldo Rio Branco de Oliveira · Real Analysis Exchange · 2014
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.