All Questions
5
questions
25
votes
1
answer
5k
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Example of fiber bundle that is not a fibration
It is well-known that a fiber bundle under some mild hypothesis is a fibration, but I don't know any examples of fiber bundles which aren't (Hurewicz) fibrations (they should be weird examples, I ...
- 253
3
votes
1
answer
443
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 are ...
- 2,064
70
votes
28
answers
7k
views
Examples where it's useful to know that a mathematical object belongs to some family of objects
For an expository piece I'm writing, it would be useful to have good examples of the following phenomenon:
(1) ${\cal X}$ is a parameterized family of somethings. (Varieties, schemes, manifolds, ...
1
vote
1
answer
661
views
An example of a space which is locally relatively contractible but not contractible?
A space $X$ is called locally contractible it it has a basis of neighbourhoods which are themselves contractible spaces. CW complexes and manifolds are locally contractible. On the other hand, the ...
- 33.2k
5
votes
2
answers
828
views
What is an example of a non-regular, totally path-disconnected Hausdorff space?
I need this for a counterexample: the multiplication in the fundamental group $\pi_1(\Sigma X_+)$, when it is equipped with the topology inherited from $\Omega \Sigma X_+$, fails to be continuous for ...
- 33.2k