Theorems · Definition · functional analysis

NormedAddCommGroup.ofCoreReplaceAll

{𝕜 : Type u_6} →
  {E : Type u_7} →
    [inst : NormedField 𝕜] →
      [inst_1 : AddCommGroup E] →
        [inst_2 : Module 𝕜 E] →
          [inst_3 : Norm E] →
            [U : UniformSpace E] →
              [B : Bornology E] →
                (core : NormedSpace.Core 𝕜 E) →
                  uniformity E = uniformity E →
                    (∀ (s : Set E), Bornology.IsBounded s ↔ Bornology.IsBounded s) → NormedAddCommGroup E

Produces a NormedAddCommGroup E instance from a NormedSpace.Core on a type that already has a preexisting uniform space structure and a preexisting bornology. This requires proofs that the uniformity induced by the norm is equal to the preexisting uniformity, and likewise for the bornology. See note [reducible non-instances].

Defined in

Mathlib.Analysis.Normed.Module.Basic

Cited by

0 results in Mathlib

Foundations

Depth 125 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldAddCommGroupModuleNormUniformSpaceBornology