Boundedness of Complex Functions

Definition: Boundedness

Let \(f: \mathcal{D} \subseteq \mathbb{C} \to \mathbb{C}\) be a complex function.

We say that \(B \gt 0\) is a bound of \(f\) on \(S \subseteq \mathcal{D}\) if

We say that \(f\) is bounded on \(S\) if it has a bound on \(S\).