$\operatorname{Isom}{(M)}$ has Lie-structure for M metrizable manifold

Question

Suppose $M$ is a smooth and metrizable manifold. Then $\operatorname{Isom}{(M)}$ can be given the structure of a Lie group, so that the action of $\operatorname{Isom}{(M)}$ on $M$ is still smooth.

I found that as a sidenote somewhere. I really would like to see a prove of the above. So if somebody happens to know an online (free accessible) source, please tell me. I know $\operatorname{Isom}{(M)}$ is locally compact w.r.t. the compact-open topology. Is this also the topology of the Lie-Group?

Answer 1

How about this, this or this?