- #1
tarheelborn
- 123
- 0
Homework Statement
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].
Homework Equations
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: