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In the earliest days of MathOverflow, there was a '20 questions' seminar (see <http://sbseminar.wordpress.com/category/20-questions/>) run by graduate students at Berkeley. Many questions from the seminar were cross-posted to MathOverflow. This tag now exists solely for the historical record.
11
votes
Accepted
What is an example of a topological space that is not homotopy equivalent to a CW-complex?
My favorite example of a space which is not homotopy equivalent to a CW complex is the Long Line. All it's homotopy groups vanish (exercise 1) but the long line is not contractible (exercise 2). It's …
7
votes
Accepted
Critical points on a fiber bundle
The part I'm still hesitant about is that the manifold you call $C$ is $n$-dimensional. Codimension arguments in the infinite dimensional setting are always a little sticky. So, I'm just going to trea …