Chapter 4.33, Problem 4E

To determine

To prove:

If $X$ is normal, there exists a continuous function $f:X\to \left[0,1\right]$ such that $f\left(x\right)=0$ for $x\in A$, and $f(x)>0$ for $x\notin A$, if and only if $A$ is a closed $G_{\delta }$ set in $X$.