Definition:Left-Total Relation/Also known as

Left-Total Relation: Also known as
A left-total relation $\RR \subseteq S \times T$ is also sometimes referred to as:
 * A total relation, but this can be confused with a connected relation
 * A relation on $S$, but this can be confused with an endorelation
 * A multiple-valued function or multifunction, but the latter is usually reserved for complex functions

The term left-total relation is usually preferred.