Open Map

Complex Analysis
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Tsakanikas Nickos
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Joined: Tue Nov 10, 2015 8:25 pm

Open Map

#1

Post by Tsakanikas Nickos »

Show that if the non constant complex-valued function \( \displaystyle f \) is defined and analytic on an open subset \( \displaystyle A \) of \( \mathbb{C} \), then \( \displaystyle f \) is an open map. That is, \( \displaystyle f \) maps open subsets of \( \displaystyle A \) to open sets.
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