Espaços uniformizáveis : teoria, equivalências e atualização

Abstract

This work presents a general study on uniform spaces motivated by recent confirmation of equivalence between the admissible and the uniformizable spaces. We will approach purely theory about uniformities by developing the theoretical aspects more relevant, discussing topological properties involved and presenting equivalences between the different ways to set them. Also, we will have the opportunity to deal with these concepts together with the theory of topological groups, which as well as the pseudometrizable case have a fundamental role since the beginning of discussions. Finally, we will do clarifications about the theory of admissible spaces together with uniformizable spaces under a new characterization of these spaces, by showing once again how much their structures coincidentally combine