The main goal of this proyect is to deepen in the study of the Convergence Spaces which are a generalization of the topological spaces, by mean of certain kinds of convergence filters. For this purpose, we are going to introduce some basic concepts in order to delve further into the properties of these spaces such as separation axioms, continuous maps or compactness. We also study two important classes, pretopological and psedotopological spaces.

Universidad de Sevilla. Grado en Matemáticas