Normality in the space of subgroups of the Lie group - Panasyuk, S. P. (Ukrains’kyi Matematychnyi Zhurnal, 1990)
It is proved that a connected Lie group is solvable if and only if the space of closed subgroups of this group is normal in the Vietoris topology and any compact segment of subgroups lying in this space is countable.