if a linear group of dimension $\geq 2$ has a dense one-parameter subgroup , then it is isomorphic to $\mathbb{T^n }$
I think it is enough to show $\mathbb{T }$ $\times$ $\mathbb{R }$ can not have dense one-parameter subgroup i try to solve it with basic topological and group theoritic facts but i cannot do it.Do i need to use analysis or something else ?