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 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.