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Sunshine-x86 (talk | contribs) Use typesetting for mathematical symbols |
Adding local short description: "Theorem on holomorphic functions", overriding Wikidata description "Theorem that holomorphic functions on complex domains are open maps" |
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{{Short description|Theorem on holomorphic functions}}
In [[complex analysis]], the '''open mapping theorem''' states that if <math>U</math> is a [[Domain (mathematical analysis)|___domain]] of the [[complex plane]] <math>\mathbb{C}</math> and <math>f: U\to \mathbb{C}</math> is a non-constant [[holomorphic function]], then <math>f</math> is an [[open map]] (i.e. it sends open subsets of <math>U</math> to open subsets of <math>\mathbb{C}</math>, and we have [[invariance of ___domain]].).
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