Grupo fundamental de espacios topológicos no euclidianos

Abstract

The study of topology is important because this field allows problems from other areas of mathematics to be solved more effectively and simply. In the study of topological spaces, the problem of classifying and identifying homeomorphic spaces arises. To address this, the theory of topological invariants is developed; however, this tool is not sufficient in some cases, so work is done to associate a group to a topological space, which is called the fundamental group. However, this study is usually developed for topological spaces with Euclidean topologies. Our objective is to study the fundamental group of certain topological spaces with non-Euclidean topologies. To do this, we will review some topics that are fundamental to the study of the fundamental group, such as connected components and path-connected components of a space, until we reach the point of knowing how to compute the fundamental group, thus gaining insight into the nature of the fundamental group of some of these spaces.