Zero set
= Zero set
{title2=$f^{-1}(\{0\})$}
The zero set of a <function> $f$ is the <preimage> $f^{-1}(\{0\})$, consisting of all its <zeros of a function>. For a real- or complex-valued <continuous function>, it is a <closed set>, because the preimage of the closed singleton $\{0\}$ under a <continuous function> is closed. A nonzero <holomorphic function> on a connected open set has isolated zeros by the <identity theorem for holomorphic functions>.