I need an example of an open set $V$ and a holomorphic function $f$ on $V$ such that $f^{'}(z)=0$ for each $z\in V$, but $f$ is not constant.
2025-01-13 05:15:58.1736745358
need an example of an open set $V$ and a holomorphic function $f$ on $V$
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You can take your open set to be two disjoint balls. Then set $f$ equal to $0$ in one of them and equal to $1$ in the other one.