= Casorati-Weierstrass theorem
{c}
{wiki=Casorati–Weierstrass_theorem}
Near an isolated <essential singularity>, a <holomorphic function> has dense image in the complex plane. If it avoided a disk about $w$, then $1/(f-w)$ would be bounded and extend across the singularity by the <Riemann removable singularity theorem>. If its extended value is nonzero, $f$ extends holomorphically; if zero, its finite-order zero makes $f$ a pole. Either contradicts an essential singularity.
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