Talk:Classifying space

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Mathematics rating:	Start Class	Mid Priority	Field: Topology
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. please add useful comments here--Cronholm144 09:50, 23 May 2007 (UTC)

Definition by homotopy groups: well, I don't think that's in good taste, and I see User:Waltpohl thinks it's suspect. So perhaps we should look to have the weak equivalence page written, which would allow one to explain why (and to what extent) anyone might come up with such a definition. Also someone to write the Eilenberg-Mac Lane space page, so we can start untangling this, without junking the intuitions right now.

Charles Matthews 11:48, 6 Sep 2004 (UTC)

I'm lost at the beginning: "It has the property that any G principal bundle over a paracompact manifold is isomorphic to a pullback of the principal bundle." A pull back induced by what map? The only map even hinted at is the quotient map, but it is not obvious how this map is related to the arbitrary paracompact manifold. Dewa (talk) 02:45, 12 April 2008 (UTC)