Zero set ($f^{-1}(\{0\})$)

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.