Thread: Holomorphic on C View Single Post
 P: 159 Suppose $f : \mathbb{C}\to \mathbb{C}$ is continuous everywhere, and is holomorphic at every point except possibly the points in the interval $[2, 5]$ on the real axis. Prove that f must be holomorphic at every point of C. How can I go from f being holomorphic every except that interval to showing it is holomorphic at that interval? I am assuming it has to be due to continuity. But there are continuous functions that aren't differentiable every where.