O teorema da função inversa e sua relação com as superfícies regulares

Abstract

This work’s main objective is to study and establish relationships between the inverse function theorem, which is presented in the Euclidean space Rn, with regular surfaces, in the context of Differential Geometry. We will show how a result arising from the context of mathematical Analysis can serve as a basis for introducing one of the main objects of study in Differential Geometry. For this construction, we will initially address basic concepts involving the topology of the Euclidean space Rn, which will be present throughout the text. Next, we will present the fundamental notions and results about continuity and differentiability in the n-dimensional Euclidean space and finally, we will introduce regular surfaces together with some relevant results to establish a natural and expected relationship with the topology of Euclidean spaces and o Inverse function theorem.