Category:Definitions/Class Mappings

This category contains definitions related to Class Mappings.
Related results can be found in Category:Class Mappings.

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

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