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'Open mapping theorem'
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| Title of object: |
Open mapping theorem |
| Canonical Name: |
OpenMappingTheorem |
| Type: |
Theorem |
| Created on: |
2002-12-07 08:59:53.575398-05 |
| Modified on: |
2002-12-07 08:59:53.575398-05 |
| Classification: |
msc:46B99, msc:30A99 |
Preamble:
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Content:
There are two important theorems having this name.
$\centerdot$ In the context of functions of a complex variable:
\textbf{Theorem.} Every non-constant analytic function on a domain is an open mapping.
$\centerdot$ In the context of functional analysis:
\textbf{Theorem.} Every surjective linear mapping between two banach spaces is an open mapping. |
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