= Normal family
{wiki}
A family $\mathcal F$ of <meromorphic functions> on a <domain> is a <normal family> if every sequence from $\mathcal F$ has a subsequence converging uniformly on every <compact subset>, measured in the <chordal metric> on the <Riemann sphere>. The <limit> is a <meromorphic function> or the constant infinity. For <holomorphic functions>, a finite <limit> is <holomorphic>; a sequence may also tend locally uniformly to infinity.
The constant <functions> $f_n(z)=n$ form a <normal family>, because any sequence has either a constant subsequence or a subsequence tending uniformly to infinity in the <chordal metric>. In contrast $g_n(z)=nz$ is not a <normal family> on any <neighbourhood> of zero. Every subsequence tends to infinity at every nonzero point but remains zero at zero; this pointwise pattern cannot be a continuous <Riemann sphere> valued <limit>.
For a <rational map> $f$, the <Fatou set> is precisely where its <iterations of a map> form a <normal family>. Normality asks for convergent subsequences, so it allows stable rotations as well as convergence to an <attracting periodic point>.<Dynamics in one complex variable: introductory lectures by John Milnor>[Section 2, normal families and Montel theory]{ref}
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