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 $\u2102\cup \{\mathrm{\infty}\}$. This point is

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

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a pole iff $\underset{z\to {z}_{0}}{lim}f(z)=+\mathrm{\infty}$,

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an essential singularity^{} iff there is neither of the above cases.
Title  Riemann’s theorem on isolated singularities^{} 

Canonical name  RiemannsTheoremOnIsolatedSingularities 
Date of creation  20130322 19:00:51 
Last modified on  20130322 19:00:51 
Owner  pahio (2872) 
Last modified by  pahio (2872) 
Numerical id  5 
Author  pahio (2872) 
Entry type  Theorem 
Classification  msc 30E99 
Synonym  Riemann’s theorem 
Related topic  RiemannsRemovableSingularityTheorem 