  A topological space $X$ is called $\Cal A$-real compact, if every algebra
homomorphism from $\Cal A$ to the reals is an evaluation at some point of $X$,
where $\Cal A$ is an algebra of continuous functions. Our main interest lies on
algebras of smooth functions. In \cite{AdR} it was shown that any separable
Banach space is smoothly real compact. Here we generalize this result to a huge
class of locally convex spaces including arbitrary products of separable
Fr\'echet spaces.
