Homework 3
This is in regards to Homework 3 Problem 4. In order to show that $ {f} $ is constant on $ \Omega $ I let $ \gamma $ be a closed circle in $ \Omega $. Knowing that $ {f} $ is analytic on $ \Omega $ we know the integral over $ \gamma $ is zero. Letting $ \omega\in\gamma $ we can set $ f(\omega)=z\in\Gamma $. My question is based on $ \rho $ and what we know about it and how it relates to $ \Gamma $ what can we know about $ f(\gamma) $? I think this will help as far as proving f is constant.
