a simple real Lie group can be seen as the space of maximal compact subgroups of the group, one can compatify this space by taking its closure in the (compact) Chabauty space of all closed subgroups. This approach is carried out by Y. Guivarc’h and the first author [@GuiRem]; it leads to statements in group theory which are analogues of [@Moore] (e.g., the virtual geometric classification of maximal amenable subgroups) but the method contains an intrinsic limitation due to which one cannot compactify more than the set of vertices of the Bruhat-Tits buildings.

The last author of the present paper also constructed compactifications of Bruhat-Tits buildings, in at least two different ways. The first way is specific to the case of the general linear group: going back to Bruhat-Tits’ interpretation of Goldman-Iwahori’s work [@GoldmanIwahori], it starts by seeing the Bruhat-Tits building of ${\rm GL}({\rm V})$ – where ${\rm V}$ is a vector space over a discretely valued non-Archimedean field – as the space of (homothety classes of) non-Archimedean norms on ${\rm V}$. The compactification consists then in adding at infinity the (homothety classes of) non-zero non-Archimedean seminorms on ${\rm V}$. Note that the symmetric space of ${\rm SL}_n({\bf R})$ is 