Suppose $M \rightarrow N$ is a continuous embedding of a topological (not necessarily smooth) manifold $M$ as a closed subset of a smooth manifold $N$. Do you know a nice way to see that $M$ is a retract of an open set in $N$? I have read that topological manifolds are absolute neighborhood retracts but I think the proof of that fact is too technical for me. I'm also aware of tubular neighborhoods but I don't see a way to produce one without a smooth structure for $M$. Thank you!
Edit: Please feel free to assume that M is compact.