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.

The well-known collar neighbourhood theorem states:

Let $M$ be a smooth manifold with compact boundary $\partial M$, then there exists a neighbourhood of $\partial M$, which is diffeomorphic to $\partial M\times [0,1)$.

I am asking myself if the theorem holds in the topological category. Is it true at least for compact topological manifolds?

My first idea would be to take a more closer look at the work of Kirby and Siebenmann on topological manifolds, but since I am absolutely not an expert in this field, I hoped to get an answer with a reference or a counterexample here.

share|improve this question

1 Answer 1

This is a special case of the main result of this paper:

Morton Brown, "Locally flat imbeddings of topological manifolds", Annals of Mathematics, Vol. 75 (1962), p. 331-341.

share|improve this answer

Your Answer

 
discard

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

Not the answer you're looking for? Browse other questions tagged or ask your own question.