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Open Mapping Theorem


Several flavors of the open mapping theorem state:

1. A continuous surjective linear mapping between Banach spaces is an open map.

2. A nonconstant analytic function on a domain D is an open map.

3. A continuous surjective linear mapping between Fréchet spaces is an open map.


See also

Analytic Function, Banach Space, Open Map

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References

Krantz, S. G. "The Open Mapping Theorem." §5.2.1 in Handbook of Complex Variables. Boston, MA: Birkhäuser, pp. 73-74, 1999.Zeidler, E. Applied Functional Analysis: Applications to Mathematical Physics. New York: Springer-Verlag, 1995.

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Open Mapping Theorem

Cite this as:

Weisstein, Eric W. "Open Mapping Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/OpenMappingTheorem.html

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