Well, definition of Lie subgroup what I know is, a Lie subgroup of a Lie group $G$ is an abstract subgroup $H$ which is an immersed submanifold via the inclusion map so that the group operations on $H$ are $C^{\infty}$.
Could any one make me understand the following with an example?
"Because a Lie subgroup is an immersed submanifold, it need not have the relative topology. In particular, the inclusion map $i:H\rightarrow G$ need not be continuous."