Definition:Bounded Metric Space/Complex/Unbounded

Definition
Let $D$ be a subset of the complex plane $\C$.

Then $D$ is unbounded (in $\C$) iff:
 * $\not \exists M \in \R: \forall z \in D: \left|{z}\right| \le M$

That is, if $D$ is not bounded in $\C$.