Let f be defined and continuous on a closed set S in R. Let A={x: x $\in$S and f(x)=0}.
Let f be defined and continuous on a closed set S in R. Let A={x: x $\in$S and f(x)=0}.
Hint: If $f$ is continues and $f(p)\not=0$ then there is an open interval such that $p\in (s,t)$ and $f$ is non-zero on $(s,t)$.