# Local Isomorphism on Lie Groups II

Yesterday I asked about an example in Chevalley's book "Theory of Lie Groups I". Well, the second example on pages 38 and 39 made me work a lot to understand.

1) First paragraph, page 39. He says that $s_{2}$$s_{1}$$r$ $\in$ $g_{1}$ implies that $r$ is in the group generated by $g_{1}$ and $g_{2}$. This must be easy to see, but I'm not convinced yet.
2) Thir paragraph. I'm not convinced that $V$ (with this condition) exists, neither why this fact implies $V$ to be mapped in a continuous univalent way by $\theta$.