Definition:Left-Total Relation/Multifunction/Branch/Principal 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 $f$ into branches.

It is usual to distinguish one such branch of $f$ from the others, and label it the principal branch of $f$.