SOUZA, J. A. S.; http://lattes.cnpq.br/5551296213160172; SOUZA, José Anderson Santos de.
Résumé:
In this paper we conducted a study on Metric Spaces presenting its definition along with
some examples and results, looking for enough tools to demonstrate the theorem from Baire.
This theorem that has applications in both Functional Analysis, how much in topology, which
highlights its importance. In order to demonstrate this, we have done the study in the theory of
spaces Metrics as: balls and spheres, limited sets, distance between point and set and between
sets. Besides these, we study sequences, as well as the topology of metric spaces, open sets and
closed sets. We also study the continuous functions, destacando a definição de homeomorfismo e
de continuidade uniforme. And so we can analyze the theorem Baire’s investigation investigated
the complete metric spaces and their relationships with the sequences of Cauchy. However,
before presenting the theorem itself and demonstrating it, we made a brief biography from
René-Louis Baire, and after that, we realize the generalization of the Interval Principle Fits in
Analysis, which is an important basic result for the theory.