A nonconstant holomorphic map sends open sets to open sets.Suggest a slogan
Let \(\Omega\subseteq\CC\) be a connected open set and let \(f\colon \Omega \to \CC\) be holomorphic and nonconstant. Then \(f\) is an open map: \(f(U)\) is open for every open set \(U\subseteq\Omega\).
State the open mapping theorem.