Given a (continuous) map $f:X\rightarrow Y$, I am looking for an evident notation for the induced map onto its image, denoted by $e$ in this diagram:
Image by Noix07
– Own work, CC BY-SA 4.0
I want to be able to write something like this, without having to explain the notation:
Let $f:X\rightarrow Y$ be a continuous map. Consider $\mathbf{?}:X\rightarrow\operatorname{im}f$. Then $\mathbf{?}$ is …
It could be something similar to $\overline{f}$ or $\tilde{f}$, but I usually preserve these for quotients, liftings etc.
I would prefer answers that also give reference to work where you have seen this notation.