# 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 OpenMappingTheorem 2013-03-22 13:12:41 2013-03-22 13:12:41 Koro (127) Koro (127) 14 Koro (127) Theorem msc 30A99 msc 46A30 ClosedGraphTheorem