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Sep 16, 2011 at 16:35 answer added Johannes Ebert timeline score: 1
Sep 16, 2011 at 16:25 comment added Will B @Oscar : That's also a great answer. If it were an answer instead of a comment, I would be torn as to whether to accept your answer or Neil's answer.
Sep 16, 2011 at 16:24 vote accept Will B
Sep 16, 2011 at 16:19 comment added Oscar Randal-Williams Re: edit. In this description, it follows that $[X, EG]$ classifies isomorphism classes of principal $G$-bundles over $X$ with a section. But these are all 1) trivial and 2) canonically isomorphic, so this is the one point set. This holds for any CW-complex $X$, so if your $EG$ is a CW-complex then $\mathrm{Id} = * \in [EG, EG]$ and it is contractible. If it is not a CW-complex you can take $X=S^n$ and deduce it is weakly contractible (there is a little basepoint subtlety here).
Sep 16, 2011 at 16:13 answer added Neil Strickland timeline score: 10
Sep 16, 2011 at 16:06 history edited Will B CC BY-SA 3.0
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Sep 16, 2011 at 15:45 answer added Fernando Muro timeline score: 1
Sep 16, 2011 at 15:37 history asked Will B CC BY-SA 3.0