Bloch's theorem (complex variables)

Bloch's theorem, which is often discussed in the context of complex analysis and the theory of analytic functions, states that if \( f \) is a holomorphic function (analytic function) defined on a simply connected open subset \( D \subset \mathbb{C} \), and if \( f \) is not constant, then for any point \( z_0 \in D \), there exists a neighborhood \( U \) of \( z_0 \) such that the image \(