Espaços de convergência e aplicações

Abstract

This dissertation investigates the theory of convergence spaces as an alter native approach to studying topological and analytical properties. In contrast to the classical approach based on neighborhoods and open sets, convergence spaces use filters and nets to define limits, offering a more flexible structure compatible with Functional Analysis and Algebraic Topology. The work pre sents a review of General Topology, exploring the transition from filters to nets, and discusses relevant applications, including the Arzel`a-Ascoli theorem and the construction of the fundamental group for limit spaces. In doing so, it aims to consolidate the importance of convergence spaces as a theoretical and practical tool for various areas of Mathematics