English
The map normedMk from an additive subgroup is surjective onto the quotient; every quotient element has a representative in the subgroup normed image.
Русский
Функция normedMk от аддитивной подгруппы сюръективна на фактор-группу: каждый элемент фактор-группы имеет образ в нормированной подгруппе.
LaTeX
$$surjective_normedMk (S) : Function.Surjective (NormedAddGroupHom.funLike.coe S.normedMk)$$
Lean4
/-- The quotient in the category of normed groups. -/
@[to_additive /-- The quotient in the category of normed groups. -/
]
noncomputable instance instNormedCommGroup [hS : IsClosed (S : Set M)] : NormedCommGroup (M ⧸ S) where
__ :=
MetricSpace.ofT0PseudoMetricSpace
_
-- This is a sanity check left here on purpose to ensure that potential refactors won't destroy
-- this important property.
