Tópicos de Variedades Diferenciables : Teorema de Sard.

Abstract

The purpose of this paper is to show the Sard's Theorem, which is an important result in the Theory of Manifolds. It tells us that every set of critical values of a smooth function has null measure. To begin with, we introduce concepts such as: smooth manifolds, smooth maps between manifolds and tangent space to a manifold at a point. Then, we introduce the concept of differentiability for a smooth map between manifolds. Furthermore, we extend the concept of sets of zero measure to the manifolds framework. Finally, we present the proof of our main result.