PlanetMath: open mapping theorem

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open mapping theorem

(Theorem)

There are two important theorems having this name.

$\bullet$ 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.

"open mapping theorem" is owned by Koro.

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Attachments:: proof of open mapping theorem (Proof) by Statusx
bounded inverse theorem (Corollary) by asteroid

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Cross-references: Banach spaces, continuous linear mapping, surjective, functional analysis, open mapping, region, analytic function, variable, complex, functions
There are 4 references to this entry.

This is version 11 of open mapping theorem, born on 2002-12-07, modified 2006-09-16.
Object id is 3675, canonical name is OpenMappingTheorem.
Accessed 5571 times total.

Classification:

AMS MSC:	46A30 (Functional analysis :: Topological linear spaces and related structures :: Open mapping and closed graph theorems; completeness )
	30A99 (Functions of a complex variable :: General properties :: Miscellaneous)

Pending Errata and Addenda

None.[ View all 3 ]

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