Suppose that $E$ is a Polish space.

Portmanteau theorem asserts that a sequence $(\mu_n)$ of Borel probability measures weakly converges to a Borel probability measure $\mu$ (shortly, $\mu_n\overset{w}{\to\mu}$) if and only if $\limsup_n \mu_n(C)\le \mu(C)$ for all closed set $C\subset E$. My question is whether there exists a countable convergence-determining class of closed sets. Namely, if there exists a countable collection $\mathcal C$ of closed subsets of $E$ such that $\limsup_n \mu_n(C)\le \mu(C)$ for all closed set $C\in\mathcal C$ implies that $\mu_n\overset{w}{\to\mu}$.