isolated singularity

Let  {}  denote the Riemann sphere, and let  U be open.  Let  f:U{}  be a function.  We say that z is an isolated singularityMathworldPlanetmath of f if there exists an open set VU containing z and such that f is analytic on  V{z}.

In other , if we take the set S of points in U where f is not analytic, the isolated singularities are exactly the isolated points of S in the usual topological sense.

There are three kinds of isolated singularities:

Title isolated singularity
Canonical name IsolatedSingularity
Date of creation 2013-03-22 14:01:04
Last modified on 2013-03-22 14:01:04
Owner bwebste (988)
Last modified by bwebste (988)
Numerical id 10
Author bwebste (988)
Entry type Definition
Classification msc 30-00