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Man, it would be really great if someone could explain why the pointwise multiplication in LG is well defined. Orthografer (talk) 15:48, 23 March 2009 (UTC)
- Multiplication in a topological group is continuous, so if you have two maps into a topological group (consider loops as maps from the 1-sphere into the space) then composing with the multiplication map yields a map which is still continuous. But I don't know whether this should be part of the article, being merely part of the definition of a topological group. Konrad (talk) 13:54, 12 May 2012 (UTC)