Talk:Extension of a topological group

Relatively open continuous homomorphism

The term "relatively open continuous homomorphism" is used in the introduction but not defined anywhere in the article or linked to a definition elsewhere: indeed, it is not mentioned anywhere else on Wikipedia. I presume that the definition being used here is that a homomorphism is relatively open if it is an open map to its image with the subset topology? This is the definition used by Bello et al. Natural boundary (talk) 06:25, 18 September 2014 (UTC)[reply]

answer: Yes, you are right, relatively open means exactly that. I've just change it. Thank you for the suggestion. (talk) — Preceding undated comment added 07:02, 18 September 2014 (UTC)[reply]

Split extensions of nonabelian groups

I'm not an expert on extensions of topological groups, but it seems to me that the statement that being a split extension is equivalent to being isomorphic to a trivial extension should only hold in the abelian category. For general groups, being a split extension is equivalent to being isomorphic to a semidirect product, and I would imagine the story isn't much different in the case of topological groups. (At least when we take discrete groups, we should recover the fact that there are split extensions--semidirect products--which are nontrivial, i.e. not direct products). Cramyam (talk) 05:02, 11 February 2021 (UTC)[reply]