Let $D$ be a non-empty connected open subset of $\mathbb{C}^n$. Let $f$ be a complex valued continuous function on $D$. Let $Z$ be the set of zeros of $f$. Suppose $f$ is holomoprphic on $D - Z$. Is $f$ holomorphic on $D$?
A complex valued continuous function which is holomorphic outside of its zeros
6
$\begingroup$
complex-analysis
several-complex-variables