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Open mapping theorem (complex analysis)

In complex analysis, the open mapping theorem states that if U {\displaystyle U} is a domain of the complex plane C {\displaystyle \mathbb {C} } and f : U → C {\displaystyle f:U\to \mathbb {C} } is a non-constant holomorphic function, then f {\displaystyle f} is an open map (i.e. it sends open subsets of U {\displaystyle U} to open subsets of C…

Applications, Proof & Overview