Zero set of a continuous function
= Zero set of a continuous function
{title2=$f^{-1}(0)$}
For a <continuous function> $f:X\to\mathbb R$, its zero set is $f^{-1}(\{0\})$. It is closed and is a <G-delta set>, since $f^{-1}(0)=\bigcap_{n\geq1}f^{-1}((-1/n,1/n))$. Replacing $f$ by $|f|/(1+|f|)$ gives the same zero set with values in $[0,1]$. In a <normal topological space>, every closed <G-delta set> has this form.