The Implicit and the Inverse Function theorems: easy proofs

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.

10 pages

References in corpus (1)

• Some Simplifications in Basic Complex Analysis

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