Casorati-Weierstrass theorem

Given a domain U, aU, and f:U{a} being holomorphic, then a is an essential singularityMathworldPlanetmath of f if and only if the image of any punctured neighborhoodMathworldPlanetmath of a under f is dense in . Put another way, a holomorphic function can come in an arbitrarily small neighborhood of its essential singularity arbitrarily close to any complex value.

Title Casorati-Weierstrass theorem
Canonical name CasoratiWeierstrassTheorem
Date of creation 2013-03-22 13:32:36
Last modified on 2013-03-22 13:32:36
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 7
Author PrimeFan (13766)
Entry type Theorem
Classification msc 30D30
Synonym Weierstrass-Casorati theorem
Related topic PicardsTheorem