Theorems · Definition · functional analysis

SeminormedAddCommGroup.ofCoreReplaceTopology

{𝕜 : Type u_6} →
  {E : Type u_7} →
    [inst : NormedField 𝕜] →
      [inst_1 : AddCommGroup E] →
        [inst_2 : Norm E] →
          [inst_3 : Module 𝕜 E] →
            [T : TopologicalSpace E] →
              (core : SeminormedSpace.Core 𝕜 E) →
                T = PseudoEMetricSpace.toUniformSpace.toTopologicalSpace → SeminormedAddCommGroup E

Produces a SeminormedAddCommGroup E instance from a SeminormedSpace.Core on a type that already has an existing topology. This requires a proof that the uniformity induced by the norm is equal to the preexisting uniformity. See note [reducible non-instances].

Defined in

Mathlib.Analysis.Normed.Module.Basic

Cited by

0 results in Mathlib

Foundations

Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldAddCommGroupNormModuleTopologicalSpace