Discussion 0 (Again): Review of Metric Spaces and Topology

In this discussion, we shall see another important object in Mathematics that is closely related to “geometry”, particularly metrics (distances). Taking a motivation from elementary calculus, we try to recall various aspects of the theory of metric spaces such as convergence of a sequence, continuity of functions, to mention a few. The main idea behind this review, however, is to understand “open sets” (and therefore, closed sets) which leads us to certain other topological concepts. The “main result”, if one wishes to take back from this discussion, would be the Urysohn’s lemma that allows us to separate certain disjoint closed sets using continuous functions.