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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6220 • Complex Analysis

Fall 2020 • Question 1

Question

Math 6220 • Complex Analysis Fall 2020 • Question 1

Let \(f_i:\mathbb {D}\to \mathbb {C}\) be a sequence of injective holomorphic functions so that \(f_i\to f_\infty \) uniformly on compact sets. If \(f_\infty \) is not injective, what can you say about it? Prove this.

Raw LaTeX

Let \(f_i:\mathbb{D}\to\mathbb{C}\) be a sequence of injective holomorphic functions so that \(f_i\to f_\infty\)
uniformly on compact sets. If \(f_\infty\) is not injective, what can you say about it?
Prove this.

Topic Tags

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