Is there a biholomorphic map between a simply connected domain and non simply connected domain?












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Is there a biholomorphic map between a simply connected domain and non simply connected domain?




I am not sure how to approach this question. This is not a homework question but one I simply came across. Perhaps we would be wise looking at the number of homology basis? Does Riemann mapping theorem work here? I have little idea of how to approach this question. I think that the open mapping theorem would be a good use, but I am not sure how to use it.










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    0












    $begingroup$



    Is there a biholomorphic map between a simply connected domain and non simply connected domain?




    I am not sure how to approach this question. This is not a homework question but one I simply came across. Perhaps we would be wise looking at the number of homology basis? Does Riemann mapping theorem work here? I have little idea of how to approach this question. I think that the open mapping theorem would be a good use, but I am not sure how to use it.










    share|cite|improve this question











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      0












      0








      0





      $begingroup$



      Is there a biholomorphic map between a simply connected domain and non simply connected domain?




      I am not sure how to approach this question. This is not a homework question but one I simply came across. Perhaps we would be wise looking at the number of homology basis? Does Riemann mapping theorem work here? I have little idea of how to approach this question. I think that the open mapping theorem would be a good use, but I am not sure how to use it.










      share|cite|improve this question











      $endgroup$





      Is there a biholomorphic map between a simply connected domain and non simply connected domain?




      I am not sure how to approach this question. This is not a homework question but one I simply came across. Perhaps we would be wise looking at the number of homology basis? Does Riemann mapping theorem work here? I have little idea of how to approach this question. I think that the open mapping theorem would be a good use, but I am not sure how to use it.







      complex-analysis holomorphic-functions






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      edited Dec 7 '18 at 21:37









      Saucy O'Path

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      asked Dec 7 '18 at 21:00









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          Simple connectedness is a topological invariant, and biholomorphisms are homeomorphisms. Therefore the answer is no.






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            $begingroup$

            Simple connectedness is a topological invariant, and biholomorphisms are homeomorphisms. Therefore the answer is no.






            share|cite|improve this answer









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              2












              $begingroup$

              Simple connectedness is a topological invariant, and biholomorphisms are homeomorphisms. Therefore the answer is no.






              share|cite|improve this answer









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                $begingroup$

                Simple connectedness is a topological invariant, and biholomorphisms are homeomorphisms. Therefore the answer is no.






                share|cite|improve this answer









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                Simple connectedness is a topological invariant, and biholomorphisms are homeomorphisms. Therefore the answer is no.







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered Dec 7 '18 at 21:03









                Saucy O'PathSaucy O'Path

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