About connected Lie Groups How can I prove that a connected Lie Group is generated by any  neighborhood of the identity?
The result is almost trivial for $R^n$ but I tried using the open subgroup generated by this neighborhood.

Is the question is similar to: Prove that any open subgroup of a connected lie group is the whole group then here is my answer, if not then please ignore it.
Take any $g\in G$ define $l_g:G\rightarrow G, l_g(k)=gk$, Let $H$ be any open subgroup of $G$,clearly as $l_g$ is a homeomorphism, and $H$ is open so $l_g(H)=gH$ is also open, but $G$ is connected so $H=G$
