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Riemann’s theorem on isolated singularities
Let the complex function $f(z)$ be holomorphic in a deleted neighbourhood of the point $z=z_{0}$ of the closed complex plane $\mathbb{C}\cup\{\infty\}$. This point is

a regular point (or a removable singularity) iff $f(z)$ is bounded in a neighbourhood of $z_{0}$,

a pole iff $\displaystyle\lim_{{z\to z_{0}}}f(z)\,=\,+\infty$,

an essential singularity iff there is neither of the above cases.
Related:
RiemannsRemovableSingularityTheorem
Synonym:
Riemann's theorem
Type of Math Object:
Theorem
Major Section:
Reference
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