Definition:Left-Total Relation/Multifunction/Branch

Definition
Let $f: \C \to \C$ be a multifunction on the complex numbers.

Let $\left \langle{S_i}\right \rangle_{i \in I}$ be a partitioning of the codomain of $\C$ such that:
 * $\forall i \in I: f \restriction_{\C \times S_i}$ is a mapping.

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