Estudo dos espaços métricos e aplicação: o teorema do ponto fixo de Brouwer

Abstract

In this work, we study metric spaces. We approach some themes like continuous applications, sequences, compact spaces and its relations to complete metric spaces, the definition of complete metric spaces using Cauchy sequences. By this way, we show that the real space, namely R, is complete, and, also Rn. We know conditions for a subset of Rn to be compact and his relation with complete metric spaces. In the last chapter, we study fixed points theory and Brouwer's fixed point Theorem, for real functions and the general case of Rn, extending by applications, based on (MARTINS; VASCONCELLOS, 2014). Furthermore, we make some observations about these extensions on the real line equipped to compactness.