Editing Montel's theorem (section)

==Locally uniformly bounded families are normal==
The first, and simpler, version of the theorem states that a family of holomorphic functions defined on an [[open set|open]] [[subset]] of the [[complex number]]s is [[normal family|normal]] if and only if it is locally uniformly bounded.

This theorem has the following formally stronger corollary. Suppose that
<math>\mathcal{F}</math> is a family of
meromorphic functions on an open set <math>D</math>. If <math>z_0\in D</math> is such that
<math>\mathcal{F}</math> is not normal at <math>z_0</math>, and <math>U\subset D</math> is a neighborhood of <math>z_0</math>, then <math>\bigcup_{f\in\mathcal{F}}f(U)</math> is dense
in the complex plane.