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For questions requesting examples of a certain structure or phenomenon

21 votes
Accepted

Example of fiber bundle that is not a fibration

$\newcommand{\RR}{\mathbb{R}} \newcommand{\To}{\longrightarrow} \newcommand{\id}{\mathrm{id}}$The example described in Tom Goodwillie's answer to a related mathoverflow question essentially solves thi …
Ricardo Andrade's user avatar
12 votes

Counterexamples in algebraic topology?

More examples of the failure of Brown representability are described by Alex Heller in the article "On the representability of homotopy functors", which provides some more fascinating insights into the …