Let $(M,d)$ be a metric space and let $\{S_n\}_n$ be a countable collection of non-empty closed and bounded subsets of $M$
Are there any additional conditions on the collection$\{S_n\}_n$ to ensure that $S:=\limsup S_n=\bigcap_n\bigcup_{m\ge n}S_m$ is closed and bounded?