Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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.

share|improve this question
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.