Metrizability in a space of subgroups of a Lie group

It is proved that a space of closed subgroups of a solvable connected Lie group in the Vietoris topology is metrizable by a complete metric. The converse is shown to be false.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 3, pp. 351–355, March, 1990.