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 
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
Explore with Wolfram|Alpha
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.Referenced on Wolfram|Alpha
Open Mapping Theorem
Cite this as:
Weisstein, Eric W. "Open Mapping Theorem."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/OpenMappingTheorem.html
Subject classifications
