Definition:Basis for Open Sets (Metric Space)

Definition
Let $M = \left({A, d}\right)$ be a metric space.

Let $\mathcal B$ be a set of open sets of $M$.

Then $\mathcal B$ is a basis for the open sets of $M$ iff:
 * for each open set $U$ of $M$, $U$ is the union of sets of $\mathcal B$.