Theorems · Definition · functional analysis

SeminormFamily.addGroupFilterBasis

{R : Type u_1} →
  {E : Type u_6} →
    {ι : Type u_9} →
      [inst : SeminormedRing R] →
        [inst_1 : AddCommGroup E] → [inst_2 : Module R E] → SeminormFamily R E ι → AddGroupFilterBasis E

The addGroupFilterBasis induced by the filter basis Seminorm.basisSets.

Defined in: Mathlib.Analysis.LocallyConvex.WithSeminorms
Cited by: 3 results in Mathlib
Foundations: Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: SeminormedRing AddCommGroup Module

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Cites12

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
SeminormedRingstatement and proof · cited by 446
SeminormFamilystatement and proof · cited by 68
AddGroupFilterBasisstatement · cited by 27
SeminormFamily.basisSetsproof · cited by 22
SeminormFamily.basisSets_nonemptyproof · cited by 0
SeminormFamily.basisSets_zeroproof · cited by 0
addGroupFilterBasisOfCommproof · cited by 0
SeminormFamily.basisSets_addproof · cited by 0
SeminormFamily.basisSets_intersectproof · cited by 0
SeminormFamily.basisSets_negproof · cited by 0

Cited by4

Results whose statement or proof uses this declaration.

SeminormFamily.moduleFilterBasisproof · cited by 10
SeminormFamily.withSeminorms_of_nhdsproof · cited by 3
SeminormFamily.basisSets_smulstatement · cited by 0
SeminormFamily.basisSets_smul_leftstatement · cited by 0