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The Fatou set of a rational map is the largest open subset of the Riemann sphere on which its iterates form a normal family. Its complement is the Julia set.

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.