Hello,

Let $G$ denote a locally compact group and $S(G)$ the chabauty space of $G$, that is the set of closed subgroups of $G$ equiped with the chabauty topology, it is a compact space.

My question is : if $G$ is a locally profinite group, for example $G=GL(n,F)$ where $F$ is a non-archimidian field, and $\mathcal{OK}(G)$ the set of open compact subgroup of $G$, it is true that $\mathcal{OK}(G)$ is closed in $S(G)$ ?

notpart of the tag. It only states the current number of questions already tagged with this tag. You can essentially ignore it. In any case, please do not include it (or create any tag that is a number except if there should be a clear mathematical meaning to it in the given context). – user9072 Jan 3 '13 at 16:29