Global Inversion of Functions: an Introduction

TL;DR

This paper provides an elementary, self-contained introduction to the basic ideas of global inverse function theorems, focusing on their foundational concepts and potential applications to differential equations.

Contribution

It offers a clear, accessible exposition of global inverse function theorems without delving into specific applications, aimed at readers interested in differential equations.

Findings

Clarifies fundamental concepts of global inverse functions

Provides a self-contained elementary exposition

Lays groundwork for applications in differential equations

Abstract

This is an exposition of some basic ideas in the realm of Global Inverse Function theorems. We address ourselves mainly to readers who are interested in the applications to Differential Equations. But we do not deal with those applications and we give a `self-contained' elementary exposition.