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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6220 • Complex Analysis

Fall 2025 • Question 2

Question

Math 6220 • Complex Analysis Fall 2025 • Question 2

Show that there is no proper holomorphic map \(f:\mathbb {D}\to \mathbb {C}\). Recall that “proper” means that \(|z_n|\to 1\) implies \(|f(z_n)|\to \infty \) for any sequence \(z_n\in \mathbb {D}\).

Raw LaTeX

Show that there is no proper holomorphic map \(f:\mathbb{D}\to\mathbb{C}\). Recall that
``proper'' means that \(|z_n|\to 1\) implies \(|f(z_n)|\to\infty\) for any sequence
\(z_n\in\mathbb{D}\).

Topic Tags

Holomorphic Functions and Cauchy-Riemann Equations Holomorphic Roots and Logarithms Zeros of Holomorphic Functions and the Identity Theorem