Let \(t \mapsto X_{t}\) be a right continuous stochastic process. Show that for closed sets \(F\)

\[\mathbb{P}\left(X_{t} \in F \quad \forall t \in \mathbb{R}^{+}ight)=\mathbb{P}\left(X_{q} \in F \quad \forall q \in \mathbb{Q}^{+}ight)\]