Tubular neighbourhood theorem

Question

in your opinion is it possible to get the existence of a tubular neighborhood for a manifold M even if it not embeds smoothly (but only topologically) in some R^N? Thank you!

Answer 1

Counterexamples mentioned in comments:

• Wild knot, obtained by connecting the endpoints of Fox-Artin arc. This is a topological embedding of $S^1$ into $\mathbb R^3$ without a tubular neighborhood.
• Alexander's horned sphere.

For more, look up wild embeddings.