Restricted image

Set

context $ f:X\to Y $
context $ S\subseteq X $
postulate $ f(S)\equiv \mathrm{im}(f|_S) $

Discussion

The notation $f(S)$ is overloading $f$, as $S$ is not actually in the domain $X$ of $f$.

Reference

Wikipedia: Image

Parents

Subset of

Image

Context

Restricted relation