open mapping theorem

There are two important theorems having this .

$\bullet$ In the context of functions of a complex variable:

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

$\bullet$ In the context of functional analysis:

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

Title	open mapping theorem
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