\begin{definition}[Definition:Basis for Open Sets (Metric Space)]
Let $M = \struct {A, d}$ be a metric space.
Let $\BB$ be a set of open sets of $M$.
Then $\BB$ is a '''basis for the open sets of $M$''' {{iff}}:
:for each open set $U$ of $M$, $U$ is the union of sets of $\BB$.
\end{definition}