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Theorems · Definition · functional analysis

SeparationQuotient.liftNormedAddGroupHomEquiv

{M : Type u_1} →
  [inst : SeminormedAddCommGroup M] →
    {N : Type u_3} →
      [inst_1 : SeminormedAddCommGroup N] →
        { f // ∀ (x : M), ‖x‖ = 0 → f x = 0 } ≃ NormedAddGroupHom (SeparationQuotient M) N

The equivalence between NormedAddGroupHom M N vanishing on the inseparable setoid and NormedAddGroupHom (SeparationQuotient M) N.

Defined in
Mathlib.Analysis.Normed.Group.SeparationQuotient
Cited by
2 results in Mathlib
Foundations
Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SeminormedAddCommGroupSeminormedAddCommGroup
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

SeparationQuotient.liftNormedAddGroupHomEquiv_symm_apply_coe · cited by 0SeparationQuotient.liftNo…SeparationQuotient.liftNormedAddGroupHomEquiv_apply · cited by 0SeparationQuotient.liftNo…DFunLike.coe · cited by 62936DFunLike.coeReal · cited by 25697RealEquiv · cited by 8337EquivNorm.norm · cited by 5413Norm.normSeminormedAddCommGroup · cited by 2671SeminormedAddCommGroupNormedAddGroupHom · cited by 216NormedAddGroupHomSeparationQuotient · cited by 128SeparationQuotientNormedAddGroupHom.comp · cited by 39NormedAddGroupHom.compSeparationQuotient.liftNormedAddGroupHom · cited by 6SeparationQuotient.liftNo…SeparationQuotient.normedMk · cited by 5SeparationQuotient.normed…SeparationQuotient.liftNormed…CITED BYCITES

Cites10

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Cited by2

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