Definition 1.5.9. Let *X* be a set, *A* ⊆ *X*, *Y* be a set, *B* ⊆ *Y*, *f* : *X* → *Y* be a function such that *f*(*A*) ⊆ *B*. We define:

Remarks.

This definition is a slight extension of `$restriction`

that simultaneously restricts the codomain to a subset `B`

of `Y`

, under the condition that the range is contained in this subset. It is compatible with the previous definition.

References.