3
votes
1answer
192 views

When is the Freudenthal compactification an ANR?

Let $X$ be a locally compact metric ANR (or, if preferred, a locally compact simplicial complex). If needed, assume that $X$ has finitely many ends or is of finite dimension. My question is: What ...
4
votes
1answer
680 views

Example in dimension theory

Could you give me an example of a complete metric space wiht covering dimension $> n$ all of which compact subsets have covering dimension $\le n$?
4
votes
3answers
479 views

Natural examples of finite dimensional spaces with interesting 2-type

Riemann surfaces provide interesting examples of 1-types - interesting as they have roles in diverse areas. However, apart from 2-dimensional lens spaces, I can't readily bring to mind natural ...
1
vote
0answers
980 views

Again about Bing's house with two rooms [duplicate]

Possible Duplicate: How to show that the “bing’s house with two rooms” is contractible? I don't know why my question is closed? here, I make my question clearly, when ...
2
votes
1answer
2k views

How to show that the “bing's house with two rooms” is contractible? [closed]

I can't image this, Someone can give a clear illustration?
18
votes
6answers
2k views

Failure of smoothing theory for topological 4-manifolds

Smoothing theory fails for topological 4-manifolds, in that a smooth structure on a topological 4-manifold $M$ is not equivalent to a vector bundle structure on the tangent microbundle of $M$. Is ...