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Relativity would make more sense down in the "In
Physics" section, in the "time" part. The thing I objected to about it being in the lead is the distracting nature of comments like "time is the 4th dimension" which combines several potentially confusing issues and providing enough information to clarify that confusion isn't appropriate in the lead. The lead should provide a clear idea of what the dimension concept is. Given the especially confusing nature of dimension for most readers (re: previous edit wars, people repeatedly editing the circle example to say its 2-dimensional, etc), IMO it makes much more sense to push concepts like time-as-an-additional-dimension to further down the article.
174:. This argument can be extended to the corresponding Stiefel manifolds of k orthonormal vectors in Hilbert space. So the historical motivation for Kuiper's theorem was that you want to think of these Stiefel spaces as approximations to the group of automorphisms of Hilbert space. But this argument (at least, framed this way) breaks down.
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Hi there. Yeah, that was one of many edits around that time. The dimension article was suffering from serious "drift" from lots of edits from various users, it was causing the article to lose focus. Bringing the reference back into the article somewhere would be fine -- IMO that comment on
General
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I believe the contractibility of the sphere in a seperable countably-infinite dimensional
Hilbert space was originally conceived of in terms of explicit homotopies between the identity, right shift and constant maps on
131:. I think the unit sphere is folklore, really, so that documenting it sensibly is a good idea; but you may be correct that the direct proof is not really notable, and certainly fallacious proofs shouldn't be here.
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84:, including removing a source. Can I ask what you disliked about the original content and whether you would object to some of it being reinstated? Thanks
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The "1" should not be italicized. Variables in this context are italicized; digits and parentheses, etc., are not.
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Spaces precede and follow the minus sign. I made them non-breakable (i.e. no line-break can appear there).
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Given your comments, you'd better look over what I have done at
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