# Continuous automorphism of a lie group in kobayashi's book

I'm reading Kobayashi's book Transformation Groups in Differential Geometry and i dont understand a thing at page 14.

My question is why $$A_\varphi$$ is continuous?

$$G$$ is a subgroup of transformation of a differentiable manifold, $$G^*$$ normal subgroup of $$G.$$

I've open Chevalley's book, Theory of Lie groups at the page 128 as Kobayashi suggested but there is nothing useful in there.

Any ideas on proving this?

• Hochschild has rewritten Chevalley's proof here, see Theorem $1$. I do not have access to Chevalley's book, but it might be that the page number is not entirely correct. Certainly the statement "there is nothing useful in there" is not correct. Not with Chevalley. – Dietrich Burde Feb 24 at 12:10
• Ok, you are right, just that dosen't help with my specific problem. – Hurjui Ionut Feb 24 at 12:18