Espaços métricos: continuidade, completude e compacidade.

Abstract

This work has as main objective to study continuity, completeness and compactness in the theory of metric spaces. A metric space is a non-empty set in which the notion of distance between its elements is well defined. The present study is interesting because the results presented here generalize some of the results observed in the theory of continuity and compactness in Euclidean spaces, Rn, with n [greater than or equal to] 1. Furthermore, these results are valid in more abstract spaces such as some sequence or function spaces, whose notion of distance escapes from intuition and entails intriguing facts, such as the fact that closed balls are not necessarily compact.