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Complex Analysis

  1. Feb 8, 2012 #1
    1. The problem statement, all variables and given/known data
    Demonstrate that a domain [itex]D\in\mathbb{C}[/itex] is simply connected if and only if, for every function [itex]f[/itex] which is analytic and free of zeroes in [itex]D[/itex], a branch of the square root of [itex]f[/itex] exists in [itex]D[/itex].


    2. Relevant equations



    3. The attempt at a solution

    I know that by definition, every function f which is analytic and free of zeroes in D, a branch of log(f(z)) exists in D and that this implies the existence of [itex]p^{th}[/itex] roots of that function. I am not sure how to get from here to square roots, though.
     
    Last edited by a moderator: Feb 9, 2012
  2. jcsd
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