For what regions $\Omega$ is the family of functions $F_{\Omega}=\cup_{n \in \mathbb{N}}\{f:f(z)=sin(nz),z \in \Omega\}$ normal?
A family $F$ is said to be normal in $n$ if every sequence $\{f_{n}\}$ of functions in $F$ contains a subsequence which converges uniformly on every compact subset of $n$.
I have problems dealing with normal families ...
Any help, please.