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How to show that there is no non-constant holomorphic function from $\Bbb{C}$ to $\Bbb{C} - \{0, 1\}$? I can only get the folowing result:

Suppose such $f$ exists, then:

  1. $f$ is unbound
  2. $1/f$ is unbound
  3. $1/(1-f)$ is unbound

But no idea to make a contradiction. Thanks!

onRiv
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    This is Picard's little theorem. It is really a non trivial result. – Mark Nov 09 '21 at 02:38
  • @Mark Oh, thanks! Can the Riemann mapping theorem be used for proving the special case? Because in my textbook the problem is an exercise in the chapter about the Riemann mapping theorem. – onRiv Nov 09 '21 at 02:42
  • @Mark Got it. Anyway I just learn Picard's little theorem and its proof. Thanks for your hint! – onRiv Nov 09 '21 at 03:01

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