What is the correct notation/terminology for the "corestriction" of a function? - MathOverflow [closed] most recent 30 from http://mathoverflow.net 2013-05-25T03:29:06Z http://mathoverflow.net/feeds/question/38608 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/38608/what-is-the-correct-notation-terminology-for-the-corestriction-of-a-function What is the correct notation/terminology for the "corestriction" of a function? Andrew Stacey 2010-09-13T19:10:24Z 2010-09-13T20:04:47Z <blockquote> <p><strong>Possible Duplicate:</strong><br> <a href="http://mathoverflow.net/questions/29911/whats-the-notation-for-a-function-restricted-to-a-subset-of-the-codomain" rel="nofollow">What&rsquo;s the notation for a function restricted to a subset of the codomain?</a> </p> </blockquote> <p>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.</p> <p>If I have a function $f \colon X \to Y$ and a subset $Z \subset X$ then I can define the <strong>restriction</strong> 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 $Y$.</p> <p>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.)</p> http://mathoverflow.net/questions/38608/what-is-the-correct-notation-terminology-for-the-corestriction-of-a-function/38616#38616 Answer by Henry Towsner for What is the correct notation/terminology for the "corestriction" of a function? Henry Towsner 2010-09-13T20:04:47Z 2010-09-13T20:04:47Z <p>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, $f|_{f^{-1}(Z)}$. </p>