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Consider a nested sequence $O_1$, $O_2$, $\dots , O_k, \dots $ of open sets in $\mathbb{Q}_p^n$ such that $O_i \setminus O_{i+1}$ has empty interior. Under which conditions do we have $\bigcap_k O_k$ open and such that $O_i \setminus \bigcap_k O_k$ has empty interior?

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    $\mathbb{Q}_p^n$ is an ultrametric space and its topology is the ultrametric topology. $\mathbb{Q}_p$ is the field of $p$-adic numbers, completion of $\mathbb{Q}$ with respect to the ultrametric topology i.e. the topology induced by the $p$-adic absolute value map.2011-10-16

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