open mapping theorem

There are two important theorems having this .

In the context of functions of a complex variable:

Theorem. Every non-constant analytic functionMathworldPlanetmath on a region is an open mapping.

In the context of functional analysisMathworldPlanetmath:

Theorem. Every surjective continuous linear mapping between two Banach spacesMathworldPlanetmath is an open mapping.

Title open mapping theoremMathworldPlanetmath
Canonical name OpenMappingTheorem
Date of creation 2013-03-22 13:12:41
Last modified on 2013-03-22 13:12:41
Owner Koro (127)
Last modified by Koro (127)
Numerical id 14
Author Koro (127)
Entry type Theorem
Classification msc 30A99
Classification msc 46A30
Related topic ClosedGraphTheorem