[Merged by Bors] - feat(analysis/normed_space): normed group hom completion #8499
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| lemma normed_group_hom.completion_def (f : normed_group_hom G H) (x : completion G) : | ||
| f.completion x = completion.map f x := rfl | ||
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| lemma normed_group_hom.completion_coe_to_fun (f : normed_group_hom G H) : |
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can you make this one a simp lemma (and then probably the simp attribute on the next one is not needed any more)?
| (h : f.surjective_on_with f.range C) : | ||
| (f.completion.ker : set $ completion G) = closure (to_compl.comp $ incl f.ker).range := | ||
| begin | ||
| by_cases Hf : ∀ x, ∥f x∥ = 0, -- This is a bit silly, we simply avoid assuming C ≥ 0 |
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couldn't you instead have a general lemma saying that, if f.surjective_on_with f.range C, then there exists a positive D such that f.surjective_on_with f.range D? Or even surjective_on_with.mono, saying that if it works for C then it works for any D \ge C?
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Great idea, thanks!
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From LTE
This used to be part of #8317