Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Fall 2008 • Question 7

Question

Math 6210 • Real Analysis Fall 2008 • Question 7

Let \(a\) be an isolated singularity of the meromorphic function \(f:\Omega \to \mathbb C\). Prove that if \(a\) is an essential singularity, then in any neighborhood of \(a\), the function \(f\) takes values arbitrarily close to any complex number.

Raw LaTeX

Let \(a\) be an isolated singularity of the meromorphic function
\(f:\Omega\to\mathbb C\). Prove that if \(a\) is an essential singularity, then in
any neighborhood of \(a\), the function \(f\) takes values arbitrarily close to any
complex number.

Topic Tags

Isolated Singularities and Residues Meromorphic Functions and Rational Functions