Talk:Hilbert's fifth problem

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This page doesn't actually state what the final resolution was (that group objects in the category of topological manifolds and actually Lie groups in a unique way). Is it worth mentioning that the assumption of any C^k-class actually leads to a real analytic (C^ω) structure. I assume this was known prior to Hilbert's question (at least for k ≥ 2). -- Fropuff 16:19, 2 November 2005 (UTC)

I have gone down with repetitive strain injury in one hand - the Devil's way of telling you about the amount of time you spend on Wikipedia. Yes; but I've got the big Soviet encyclopedia open now, and it says the same things, really. A sharper statement: any locally compact group and any neighbourhood of e in it contains an open set K × L where K is a compact subgroup and L a local Lie group. This gives Hilbert 5 when combined with 'no small subgroups'. Charles Matthews 16:45, 2 November 2005 (UTC)

[edit] recent addition of WAREL

Well finally WAREL has added something with a reference that is capable of being followed up. However I note that his/her text is copied directly from here, and the reference looks to be copied character-for-character from here. I am not knowledgeable in this area, perhaps someone with more background can clarify the relation of Yamabe's work with the material already in the article. Dmharvey 04:13, 8 March 2006 (UTC)

That statement "the group axioms collapse the whole C^k gamut" is confusingly phrased.143.167.237.208 10:41, 21 June 2006 (UTC)