O Teorema de Eberlein-mulian e algumas aplicações

Abstract

The main objective of this dissertation is to detail the proof of the Eberleinmulian Theorem and present some applications. We begin this work by recalling results that will be useful in the development of the dissertation. In Chapter 2, we present several results on weak and weak star topologies. In particular, we study the compactness and sequential compactness of sets in these topologies. In Chapter 3, the metrizability of the weak and weak-star topologies is studied and the proof of the Eberlein-mulian Theorem is presented. We conclude this work by presenting two applications of this result; the Dunford-Pettis Theorem and the Krein-mulian Theorem.