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Is there a standard notation for a self map? i.e. for a map $$f : U \rightarrow U$$ We can describe $f$ in words as a map on $U$ or a self-map on $U$.

But is there an accepted mathematical notation for this that doesn't involve writing $U$ twice? Maybe a kind of hooked arrow like this:

$$f : U \circlearrowleft$$

Except shaped more like the $\supset$ symbol. I wasn't able to find anything with a quick Google search, and couldn't find anything appropriate on detexify.

Myridium
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    A "self-map" $f$ is an endomorphism. A possible notation for that would be $f\in End(U)$. – Mirko Apr 03 '17 at 14:05
  • I don't think there is a standard way to do this symbolically. What is so wrong with $f\colon U\to U$? I personally think you should avoid as much as you can to introduce unnecessary notation. – Shoutre Apr 03 '17 at 14:14
  • @Shoutre - it can become messy when the space $U$ is written explicitly as a long expression. – Myridium Apr 03 '17 at 14:18
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    Then you could for instance set, say $C$ as a short for your complicated space and still write $f\colon C\to C$. I believe this is more or less standard. My point is that I think there is no standard symbolic way of doing this. – Shoutre Apr 03 '17 at 14:27

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