Restorability of the Vietoris topology according to the compacts in the space of closed subgroups - Piskunov, A. G. (Ukrains’kyi Matematychnyi Zhurnal, 1990)
It is proved that the space of closed subgroups ${\mathfrak L} (G)$ of a locally compact $σ$-compact group $G$ is a $k$-space if and only if each noncompact subgroup of $G$ can be represented as the intersection of a countable number of open sets.