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?