Corrected automatic continuity conditions for finite-dimensional representations of connected Lie groups

We continue the study of automatic continuity conditions for finite-dimensional representations of connected Lie groups. In particular, we claim that every locally bounded finite-dimensional representation of a connected Lie group is continuous on the commutator subgroup in the intrinsic Lie topology of the subgroup and continuous on the intersection of the commutator subgroup with the radical of the group in the original topology of the Lie group, thus correcting one of our previous results.