I’m willing to bet that most students who have used Rudin’s Principles of Mathematical Analysis have encountered this problem: 15. Call a mapping of \(X\) into \(Y\) open if \(f(V)\) is an open set in \(Y\) whenever \(V\) is an open set in \(X\). Prove that every continuous open mapping of \(\mathbb{R}\) into \(\mathbb{R}\) is […]