Talk:Classifying space for U(n)

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I removed the stuff that ES^1 is a unit sphere in Hilbert space (kinda projective limit of finite-dim spaces), instead inserting CP^\infty (inductive limit). 18.87.0.72 04:02, 31 October 2005 (UTC)

Seems like the same thing to me, isn't it? linas 07:04, 1 November 2005 (UTC)
Not at all. The only complex projective space that is ismorphic to a shpere is CP(1). If I remember well, the unit sphere in a Hilbert space is contractible (please correct me if I'm wrong or write a reference if you know one) whereas CP^\infty has its cohomology isomorphic to \mathbb{R}[X^2]. S.racaniere 23:47, 30 December 2006 (UTC)
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