Theorems · Definition · functional analysis

PseudoMetricSpace.ofSeminormedSpaceCore

{𝕜 : Type u_6} →
  {E : Type u_7} →
    [inst : NormedField 𝕜] →
      [inst_1 : AddCommGroup E] →
        [inst_2 : Norm E] → [inst_3 : Module 𝕜 E] → SeminormedSpace.Core 𝕜 E → PseudoMetricSpace E

Produces a PseudoMetricSpace E instance from a SeminormedSpace.Core. Note that if this is used to define an instance on a type, it also provides a new uniformity and topology on the type. See note [reducible non-instances].

Defined in

Mathlib.Analysis.Normed.Module.Basic

Cited by

0 results in Mathlib

Foundations

Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldAddCommGroupNormModule