Theorems · Definition · functional analysis
SeminormFamily.moduleFilterBasis
{𝕜 : Type u_2} →
{F : Type u_7} →
{ι : Type u_9} →
[inst : NormedDivisionRing 𝕜] →
[inst_1 : AddCommGroup F] → [inst_2 : Module 𝕜 F] → SeminormFamily 𝕜 F ι → ModuleFilterBasis 𝕜 FThe moduleFilterBasis induced by the filter basis Seminorm.basisSets.
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- NormedDivisionRingstatement and proof · cited by 360
- SeminormFamilystatement and proof · cited by 68
- AddGroupFilterBasisproof · cited by 27
- ModuleFilterBasisstatement · cited by 9
- SeminormFamily.addGroupFilterBasisproof · cited by 3
- SeminormFamily.basisSets_smul_leftproof · cited by 0
Cited by12
Results whose statement or proof uses this declaration.
- WithSeminorms.topologicalAddGroupproof · cited by 11
- SeminormFamily.withSeminorms_iff_nhds_eq_iInfproof · cited by 8
- WithSeminorms.hasBasisproof · cited by 5
- WithSeminorms.topology_eq_withSeminormsstatement · cited by 5
- SeminormFamily.withSeminorms_of_nhdsstatement and proof · cited by 3
- WithSeminorms.congrproof · cited by 3
- WithSeminorms.withSeminorms_eqstatement · cited by 2
- SeminormFamily.filter_eq_iInfstatement · cited by 1
- WithSeminorms.toLocallyConvexSpaceproof · cited by 1
- WithSeminorms.continuousSMulproof · cited by 0
- WithSeminorms.recOnstatement and proof · cited by 0
- WithSeminorms.casesOnstatement and proof · cited by 0