In my book on lie algebras, it is written the following stuff :
Let $G$ be a Lie group, $H$ a Lie subgroup of G.
$G/H$ is then a manifold.
Is it hard to prove ?
It is a little abstract for me : $G/H$ could not be "smooth" in my vision (we could have like a discrete set of elements, so we could'nt find open sets to define the charts). But it seems it's not the case.
But I don't have any idea to how to prove this.
(I'm a huge beginner in group theory and in Lie groups, I just started to learn this)