instSeminormedCommGroup — Mathlib

English

normedMk is surjective from AddSubgroup to the quotient normed elements.

Русский

Функция normedMk отображает нормируемые элементы подгруппы S на все элементы факторгруппы эффективно.

LaTeX

$$surjective_normedMk (S) : Function.Surjective (normedMk S)$$

Lean4

/-- The seminormed group structure on the quotient by a subgroup. -/
@[to_additive /-- The seminormed group structure on the quotient by an additive subgroup. -/
    ]
noncomputable instance instSeminormedCommGroup : SeminormedCommGroup (M ⧸ S)
    where
  toUniformSpace := IsTopologicalGroup.toUniformSpace (M ⧸ S)
  __ := groupSeminorm.toSeminormedCommGroup
  uniformity_dist := by
    rw [uniformity_eq_comap_nhds_one', (nhds_one_hasBasis.comap _).eq_biInf]
    simp only [dist, preimage_setOf_eq, norm_eq_groupSeminorm, map_div_rev]

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