MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).

## What is the correct notation/terminology for the “corestriction” of a function? [closed]

Possible Duplicate:
What’s the notation for a function restricted to a subset of the codomain?

This is a really simple notation/terminology question, but I want to talk about it in a lecture tomorrow so want to be sure I'm using the right name.

If I have a function $f \colon X \to Y$ and a subset $Z \subset X$ then I can define the restriction of $f$ to $X$ and it can be written $f |_Z \colon Z \to Y$. What I want to know is whether or not there is an official name (or "widely accepted" name) and notation for when one restricts the function based on the target space. That is, when we have $Z \subseteq Y$ (containing $\operatorname{im} f$, of course) and restrict the codomain of $f$ to $Z$ instead of $Y$.

Nothing springs to mind, and it's hard to google something that you don't know the name of! (A few obvious ones didn't bring up anything.)

-
mathoverflow.net/questions/29911/… – Dan Petersen Sep 13 2010 at 20:07
"constriction", perhaps? – Terry Tao Sep 13 2010 at 20:21
@Dan: Thanks! Missed that one (and it didn't come up in the suggestions). I'll (vote to) close as a duplicate. – Andrew Stacey Sep 13 2010 at 20:22
"$f: X\to Y$ factors through $Z \subseteq Y$"? – Theo Johnson-Freyd Sep 13 2010 at 20:32

## closed as exact duplicate by Andrew Stacey, Theo Johnson-Freyd, Ben Webster♦Sep 13 2010 at 21:13

I usually call the corresponding subset of $X$ the inverse image of $Z$, denoted $f^{-1}(Z)$. But I can't recall seeing a standard notation (other than the obvious, but a bit over-complicated, $f|_{f^{-1}(Z)}$.
 I think in OP's case $Z \supseteq f(X)$. – Theo Johnson-Freyd Sep 13 2010 at 20:31