How do I prove that $\mathbb R^\omega$ with the box-topology (i.e., the basis are of the form $\prod_n G_n$, where $G_n$ are open in $\mathbb R$) is Completely Regular (i.e. Given a point $a$ and a closed set $F$; one can find a continuous function $f:\mathbb R^\omega \to [0,1]$ such that $f(a)=0$ and $f(F)=1$). Thank you.
Note: It is not known whether $\mathbb R^\omega$ with the box-topology is Normal.