Talk:Closed-subgroup theorem

Something wrong in the informal description

Condition (1) of the informal description's first paragraph states

"log(e^H) = H, H ∈ U (1)"

How can this be right? H is a subgroup, so it has the wrong type to be a member of an open set of group elements. Also, I think the style of writing "proposition(v), condition(v)" as a shorthand for "proposition(v) for all v such that condition(v)" is a very bad idea. It should be spelled out in words, per WP:TECHNICAL: we should not be writing this in a style that puts obstacles in the way of reading for people who do not already understand this material well. —David Eppstein (talk) 06:58, 18 July 2014 (UTC)

I really agree about the style. Some of the ladies in my grandmother's bridge club were discussing just this point. "EEng", said Mrs. Abramowitz, "we got as far as embedded submanifolds always having the subspace topology, but after that we were really stumped. This should really be written more for people who don't already understand this kind of material well. Sheila, weren't you just saying that it would help if von Neumann's proof for the special case of groups of linear transformations was explained first? Five no-trump." EEng (talk) 11:06, 18 July 2014 (UTC)

I was following Rossmann's style. He hates wasting alphabetical resources almost as much as he hates parentheses and consistently uses H ∈ h (element of Lie algebra) and h ∈ H (element of the corresponding Lie group), sometimes within one single equation. I agree with the objections against "proposition(v), condition(v)" and Rossmann's style. But I don't think the proof should go before the informal description of what the problem is with general subgroups. YohanN7 (talk) 15:28, 18 July 2014 (UTC)

Please tell me you knew I was kidding. EEng (talk) 15:59, 18 July 2014 (UTC)

Your grandmothers friends are to be taken seriously. They probably knew both von Neumann and Cartan in their youth, or, at least, went to the same nightclubs as them. YohanN7 (talk) 17:54, 18 July 2014 (UTC)

Oh, the stories these gals tell! Apparently one of them was present at Abel's duel. And that Poincaré was a real partier. The time they accidentally invited Gauss and Lobachevsky to the same dinner -- whoa! The fur really flew then! See [1]. EEng (talk) 18:18, 18 July 2014 (UTC)