Theorems · Theorem · functional analysis

NormedAddGroupHom.ker_completion

∀ {G : Type u_1} [inst : SeminormedAddCommGroup G] {H : Type u_2} [inst_1 : SeminormedAddCommGroup H]
  {f : NormedAddGroupHom G H} {C : ℝ},
  f.SurjectiveOnWith f.range C →
    ↑f.completion.ker = closure ↑(NormedAddCommGroup.toCompl.comp (NormedAddGroupHom.incl f.ker)).range

Defined in: Mathlib.Analysis.Normed.Group.HomCompletion
Cited by: 0 results in Mathlib
Foundations: Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: SeminormedAddCommGroup SeminormedAddCommGroup

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