Definition:Left-Total Relation/Multifunction/Branch

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

Let $f: D \to \C$ be a multifunction on $D$.

Let $\family {S_i}_{i \mathop \in I}$ be a partitioning of the codomain of $f$ such that:
 * $\forall i \in I: f \restriction_{D \times S_i}$ is a mapping.

Then each $f \restriction_{D \times S_i}$ is a branch of $f$.