Open mapping theorem (complex analysis)

The open mapping theorem, sometimes set by the open mapping, is a set of function theory and states that images of open sets, re- open under holomorphic maps which are constant on any connected component of the open set. One implication of this sentence is the maximum principle for holomorphic functions. Higher-Dimensional statements of this nature do not apply.

The set of open figure for holomorphic functions

Be open and a holomorphic function which is constant on any connected component of. Then is an open set.

An immediate consequence is the area fidelity of holomorphic functions.

Be a non-constant holomorphic function on a field, then is also an area.

Swell

• George Marinescu: function theory. Lecture notes in 2009, University of Cologne, pp. 41-42
• Eberhard Friday, Rolf Busam: Function Theory 1 Springer 2006, ISBN 9783540317647, pp. 123 (restricted online version in the Google Book Search )

• Function theory
• Set ( mathematics)