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

• a regular point (or a removable singularity) iff $f(z)$ is bounded in a neighbourhood of $z_0$,

• a pole iff  $\underset{z\to z_0}{lim}|f(z)|=+\mathrm{\infty }$,

• an essential singularity iff there is neither of the above cases.

Title	Riemann’s theorem on isolated singularities
Canonical name	RiemannsTheoremOnIsolatedSingularities
Date of creation	2013-03-22 19:00:51
Last modified on	2013-03-22 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