I'm trying to solve this exercise: Let G⊂GL(n,R) be a subgroup. Prove that G is a Lie group if and only if it is a closed subset of GL(n,R) in the relative topology.
I thing I have to use the fact that G is a subgroup hence the multiplication is closed as an operation in G in order to show it is also a closed set in the topological sense, but I'm stuck here. Any suggestions (also for the other direction) ? Thanks in advance.