A family $\mathcal F$ of holomorphic or meromorphic functions on a domain $U$ is a <normal family> if every sequence in $\mathcal F$ has a subsequence converging locally uniformly in the spherical metric to a meromorphic function or to infinity. <Montel theorem> states that a family of meromorphic functions omitting three fixed points of the Riemann sphere is normal; for plane-valued holomorphic functions, two omitted values suffice.

Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 157 / 1 / a / Solution

 Solution (source code)