The following theorem is in the functional analysis literature generally referred to as the Schauder lemma. It is a version of the open mapping theorem in Fréchet spaces and is often used to verify the open-ness of linear, continuous maps.
Theorem. Let be Fréchet spaces. Denote by the zero neighborhood filter of and respectively. Let be a linear and continuous map which is almost open, i.e.
Then is open.
|Date of creation||2013-03-22 19:09:44|
|Last modified on||2013-03-22 19:09:44|
|Last modified by||karstenb (16623)|
|Defines||almost open set|