Let \(f\) be an entire function with the property that \(f^{-1}(B)\) is bounded or empty for every \(B\subset \mathbb C\) bounded. Prove that \(f(\mathbb C)=\mathbb C\).
Question
Math 6210 • Real Analysis
Fall 1994 • Question 8
Question
Fall 1994 • Question 8
Let \(f\) be an entire function with the property that \(f^{-1}(B)\) is bounded or empty for every \(B\subset \mathbb C\) bounded. Prove that \(f(\mathbb C)=\mathbb C\).