Let $f: \Omega \to \mathbb{C}$ be a holomorphic function, if $f$ is not identically zero, then we can find an open set $U$ on which $f$ is nonzero. why is that?
Thank you!
Let $f: \Omega \to \mathbb{C}$ be a holomorphic function, if $f$ is not identically zero, then we can find an open set $U$ on which $f$ is nonzero. why is that?
Thank you!
Because $f$ is continuous and $\Bbb C\setminus\{0\}$ is open.