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Möbius Transformations <=> holomorphic and 1-to-1?

  1. Feb 2, 2014 #1
    So every Möbius transformation of the complex plane is holomorphic and 1-to-1 on the Riemann sphere. Is the converse also true, or are there counter-examples?
     
  2. jcsd
  3. Feb 4, 2014 #2

    mfb

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