Is there a holomorphic and bijective function of the unit disc onto the complex plane?

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Is there a holomorphic and bijective function between the open unit ball of $mathbbC$ and $mathbbC$?



The usual homeomorphisms $psi(z):=fracz$ and his composition with the conjugate map are not holomorphic on $mathbbC$.






complex-analysis holomorphic-functions







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    up vote
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    down vote

    favorite












    Is there a holomorphic and bijective function between the open unit ball of $mathbbC$ and $mathbbC$?



    The usual homeomorphisms $psi(z):=fracz$ and his composition with the conjugate map are not holomorphic on $mathbbC$.






    complex-analysis holomorphic-functions







    share|cite|improve this question

























      up vote
      1
      down vote

      favorite









      up vote
      1
      down vote

      favorite











      Is there a holomorphic and bijective function between the open unit ball of $mathbbC$ and $mathbbC$?



      The usual homeomorphisms $psi(z):=fracz$ and his composition with the conjugate map are not holomorphic on $mathbbC$.






      complex-analysis holomorphic-functions







      share|cite|improve this question















      Is there a holomorphic and bijective function between the open unit ball of $mathbbC$ and $mathbbC$?



      The usual homeomorphisms $psi(z):=fracz$ and his composition with the conjugate map are not holomorphic on $mathbbC$.






      complex-analysis holomorphic-functions




      complex-analysis holomorphic-functions






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      share|cite|improve this question













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      edited 16 mins ago









      Giuseppe Negro

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      16.5k328119










      asked 18 mins ago









      Federico Fallucca

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      1,42618




















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          No, because its inverse would be a holomorphic map from $mathbb C$ to the open unit disk on $mathbb C$. Therefore, it would be bounded and then, by Liouville's theorem, it would be a constant map.






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          • Sorry. I asked a stupid question.
            – Federico Fallucca
            7 mins ago










          • I don't think so.
            – José Carlos Santos
            4 mins ago










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          up vote
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          No, because its inverse would be a holomorphic map from $mathbb C$ to the open unit disk on $mathbb C$. Therefore, it would be bounded and then, by Liouville's theorem, it would be a constant map.






          share|cite|improve this answer




















          • Sorry. I asked a stupid question.
            – Federico Fallucca
            7 mins ago










          • I don't think so.
            – José Carlos Santos
            4 mins ago














          up vote
          4
          down vote













          No, because its inverse would be a holomorphic map from $mathbb C$ to the open unit disk on $mathbb C$. Therefore, it would be bounded and then, by Liouville's theorem, it would be a constant map.






          share|cite|improve this answer




















          • Sorry. I asked a stupid question.
            – Federico Fallucca
            7 mins ago










          • I don't think so.
            – José Carlos Santos
            4 mins ago












          up vote
          4
          down vote










          up vote
          4
          down vote









          No, because its inverse would be a holomorphic map from $mathbb C$ to the open unit disk on $mathbb C$. Therefore, it would be bounded and then, by Liouville's theorem, it would be a constant map.






          share|cite|improve this answer












          No, because its inverse would be a holomorphic map from $mathbb C$ to the open unit disk on $mathbb C$. Therefore, it would be bounded and then, by Liouville's theorem, it would be a constant map.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered 16 mins ago









          José Carlos Santos

          125k17101188




          125k17101188











          • Sorry. I asked a stupid question.
            – Federico Fallucca
            7 mins ago










          • I don't think so.
            – José Carlos Santos
            4 mins ago
















          • Sorry. I asked a stupid question.
            – Federico Fallucca
            7 mins ago










          • I don't think so.
            – José Carlos Santos
            4 mins ago















          Sorry. I asked a stupid question.
          – Federico Fallucca
          7 mins ago




          Sorry. I asked a stupid question.
          – Federico Fallucca
          7 mins ago












          I don't think so.
          – José Carlos Santos
          4 mins ago




          I don't think so.
          – José Carlos Santos
          4 mins ago

















           

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