Riemann’s removable singularity theorem

Let U be a domain, aU, and let f:U{a} be holomorphic. Then a is a removable singularityMathworldPlanetmath of f if and only if


In particular, a is a removable singularity of f if f is http://planetmath.org/node/BoundedPlanetmathPlanetmathPlanetmathbounded near a, i.e. if there is a punctured neighborhood V of a and a real number M>0 such that |f(z)|<M for all zV.

Title Riemann’s removable singularity theorem
Canonical name RiemannsRemovableSingularityTheorem
Date of creation 2013-03-22 13:33:00
Last modified on 2013-03-22 13:33:00
Owner pbruin (1001)
Last modified by pbruin (1001)
Numerical id 4
Author pbruin (1001)
Entry type Theorem
Classification msc 30D30
Related topic Pole
Related topic EssentialSingularity
Related topic Meromorphic
Related topic RiemannsTheoremOnIsolatedSingularities