On the Space of Left-Orderings of Virtually Solvable Groups - Rivas-Espinosa, C (European Mathematical Society Publishing House, 2016)
We show that the space of left-orderings of a countable virtually solvable group is either finite or homeomorphic to a Cantor set. We also provide an explicit description of the space of left-orderings of SOL = Z2 ⋊ T Z.