The space of closed subgroups of R-n is stratified and simply connected

摘要

The Chabauty space of a topological group is the set of its closed subgroups, endowed with a natural topology. As soon as n > 2, the Chabauty space of R-n has a rather intricate topology and is not a manifold. By an investigation of its local structure, we fit it into a wider, but not too wild, class of topological spaces (namely, Coresky-MacPherson stratified spaces). Thanks to a localization theorem, this local study also leads to the main result of this article: the Chabauty space of R-n is simply connected for all n.