Talk:Hilbert's fifth problem

message: 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)
thread_title:  recent addition of WAREL 

message: This entry's content is really messy, reflecting perhaps the present state of the theory around the topic dealt. However, since I cannot work on it now, I decided to collect here some advice for the ones who can (and eventually for me, in the not so next future. :D ):
#A more elementary definition of the problem in the introduction: without emphasizing its importance in theoretical physics, geometry and other branches of mathematical and natural sciences, the essence of the problem should be exposed in the most simple (however confusing) terms, closely to Hilber's original formulation.
#The historical approach: a chronology of all contribution and claims should be created, with precise references and notes, starting from Hilbert, Von Neumann, Pontryagin, Montgomery and Zippin, Yamabe and Rosinger. A differences in the formulation of the problem should be sketched in this section: also it would be important to consider survey papers, such as the ones of C.T. Chang in the noted book on Hilbert's problems published by the American Mathematical Society, and the one of J. Hirschfeld in the Transactions of the AMS.
#The "Formal definition" section: this section should be as precise as possible, presenting all the approaches sketched in the historical section in a formally precise Definition-Theorem way. Obviously, proofs should be avoided as lengthy and not trivial, but maybe a sketch of them should be included.
#Applications: descriptions of why the problem is important should be included.
Well, I hope this list will be of some help to someone (maybe even me, :D ) who wants to improve the entry on this interesting topic. Daniele.tampieri (talk) 20:19, 15 September 2011 (UTC)
thread_title:  On the state of this entry. 

message: http://terrytao.wordpress.com/books/hilberts-fifth-problem-and-related-topics/
69.111.193.46 (talk) 08:41, 2 April 2012 (UTC)
thread_title:  textbook draft 

message: The first sentence of the section Classical formulation is as follows:
"A formulation that was accepted for a long period was that the question was to characterize Lie groups as the topological groups that were also topological manifolds."
By describing the problem in such vague terms, this description avoids focusing on what the problem is.
The fact that the problem is restated later in the same section is no reason not to improve this first sentence.
I hope someone familiar with the problem can rewrite the sentence crisply and clearly so that the nature of the problem is clear. 2601:200:C000:1A0:6C9E:36DF:DC73:342E (talk) 01:26, 2 September 2021 (UTC)
thread_title:  Needs a much bettter description of the problem 

message: In the article it is said:
If we consider a general locally compact group  and the connected component of the identity , we have a group extension  As a totally disconnected group,  has an open compact subgroup, and the pullback  of such an open compact subgroup is an open, almost connected subgroup of . In this way, we have a smooth structure on , since it is homeomorphic to , where  is a discrete set.
And something is wrong here. If I take G to be the p-adic integers, then the connected component G0 is just {0}. So, G/G0 is just G. Since G/G0 is compact, we can take G′ to be G as well. Now, the article claims that  is discrete, but that is not true, because that is again just G and G is not discrete (as it is infinite and compact). So, something is wrong here...
Or am I missing something? --2003:C9:7F2D:3097:D814:2968:9A79:E173 (talk) 09:58, 9 April 2022 (UTC)
replies: text: I agree this cannot be correct. It is probably supposed to be a proof of the claim just above, that "any almost connected l.c. group is a projective limit of Lie groups", but the argument should use that G/G_0, being compact and totally disconnected, is a projective limit of finite groups and then construct Lie groups from G_0 and these finite groups such that G is the projective limit of these. This does not seem completely obvious to me, and in any case there should be a proper reference there instead. jraimbau (talk) 12:51, 10 April 2022 (UTC)

text: I made some changes and added references to Tao's book. I think the article is still not in an acceptable state ; at least  there should be a more complete discussion of the Montgomery--Zippin--Gleason solution in a section and more detailed comments on the Gleason--Yamabe results on lc groups (including examples) in another. jraimbau (talk) 15:49, 12 April 2022 (UTC)
thread_title:  Possible Error in the article