Definition:Mapping/Class Theory

Definition
Let $V$ be a basic universe.

Let $A \subseteq V$ and $B \subseteq V$ be classes.

In the context of class theory, a mapping from $A$ into $B$ is a relation $f \subseteq A \times B$ such that:


 * $\forall x \in A: \exists! y \in B: \tuple {x, y} \in f$

That is:
 * $\forall x \in A: \forall y_1, y_2 \in B: \tuple {x, y_1} \in f \land \tuple {x, y_2} \in f \implies y_1 = y_2$

and
 * $\forall x \in A: \exists y \in B: \tuple {x, y} \in f$