Theorems · Definition · functional analysis

SeminormFamily.sigma

{𝕜 : Type u_2} →
  {E : Type u_6} →
    {ι : Type u_9} →
      [inst : NormedField 𝕜] →
        [inst_1 : AddCommGroup E] →
          [inst_2 : Module 𝕜 E] →
            {κ : ι → Type u_11} → ((i : ι) → SeminormFamily 𝕜 E (κ i)) → SeminormFamily 𝕜 E ((i : ι) × κ i)

(Disjoint) union of seminorm families.

Defined in: Mathlib.Analysis.LocallyConvex.WithSeminorms
Cited by: 3 results in Mathlib
Foundations: Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedField AddCommGroup Module

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Modulestatement and proof · cited by 20,661
AddCommGroupstatement and proof · cited by 12,871
NormedFieldstatement and proof · cited by 1,084
Seminormproof · cited by 272
SeminormFamilystatement and proof · cited by 68

Cited by3

Results whose statement or proof uses this declaration.

withSeminorms_iInfstatement and proof · cited by 3
withSeminorms_pistatement · cited by 3
ContDiffMapSupportedIn.withSeminormsproof · cited by 1