Open mapping theorem (complex analysis): Difference between revisions

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{{Otheruses|Open mapping theorem}}

In [[complex analysis]], the '''open mapping theorem''' states that if ''U'' is a [[Domain (mathematical analysis)|___domain]] of the [[complex plane]] '''C''' and ''f'' : ''U'' → '''C''' is a non-constant [[holomorphic function]], then ''f'' is an [[open map]] (i.e. it sends open subsets of ''U'' to open subsets of '''C''', and we have [[invariance of ___domain]].).