For each closed set $A\subseteq\mathbb{R}$, is it possible to construct a real continuous function $f$ such that the zero set, $f^{-1}(0)$, of $f$ is precisely $A$, and $f$ is infinitely differentiable on all of $\mathbb{R}$?
Thanks!
For each closed set $A\subseteq\mathbb{R}$, is it possible to construct a real continuous function $f$ such that the zero set, $f^{-1}(0)$, of $f$ is precisely $A$, and $f$ is infinitely differentiable on all of $\mathbb{R}$?
Thanks!