An essential singularity cannot omit three spherical values: omitting three forces meromorphic extension.Suggest a slogan
Let \(z_0\in\CC\), let \(\delta>0\), and let \(f\) be meromorphic on the punctured disc \(\{z : 0<\abs{z-z_0}<\delta\}\). If there are three distinct points of \(\CC\cup\{\infty\}\) that \(f\) does not take on this punctured disc, then \(f\) extends to a meromorphic function on the disc \(\{z : \abs{z-z_0}<\delta\}\).