Talk:Topological group

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Mathematics rating:	Start Class	High 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. Rewrite of the lead would help. Geometry guy 22:21, 17 June 2007 (UTC)

Is it OK to say that 'Continuous group' is the same than 'Topological group' ??

looxix 23:30 Feb 23, 2003 (UTC)

Continuous group is an older term that possibly could also mean Lie group, so I would be careful. AxelBoldt 21:16 Mar 2, 2003 (UTC)

Although it is true that the left uniformity turns left multiplications into uniformly continuous maps, this is not a characterization of the left uniformity. In fact, the right uniformity also turns left multiplications into uniformly continuous maps. The important characteristic of the left uniformity is that it is invariant with respect to left translations. This is not mentioned on the page.

[edit] objects in analysis

"Almost all objects investigated in analysis are topological groups (usually with some additional structure)."

The above statement, which appears at the beginning of the article, is ambiguous. For example, continuous functions, open sets, and Lebesgue measure are not topological groups in any reasonable sense. Can someone rephrase the sentence? --Acepectif 03:45, 19 June 2007 (UTC)

After the remark that the fundamental group of a topological group is abelian, this is deduced from the corresponding property for H-spaces. This is silly: the proof for topological groups works the same way and is simpler, so H-spaces introduce needless generality.