Theorems · Theorem · functional analysis
SeminormFamily.basisSets_mem
∀ {R : Type u_1} {E : Type u_6} {ι : Type u_9} [inst : SeminormedRing R] [inst_1 : AddCommGroup E] [inst_2 : Module R E]
(p : SeminormFamily R E ι) (i : Finset ι) {r : ℝ}, 0 < r → (i.sup p).ball 0 r ∈ p.basisSets- Cited by
- 6 results in Mathlib
- Foundations
- Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- Modulestatement and proof · cited by 20,661
- Finsetstatement and proof · cited by 13,712
- AddCommGroupstatement and proof · cited by 12,871
- Finset.supstatement · cited by 530
- SeminormedRingstatement and proof · cited by 446
- Seminormstatement · cited by 272
- Seminorm.ballstatement · cited by 78
- SeminormFamilystatement and proof · cited by 68
- SeminormFamily.basisSetsstatement · cited by 22
- SeminormFamily.basisSets_iffproof · cited by 16
Cited by6
Results whose statement or proof uses this declaration.
- WithSeminorms.isVonNBounded_iff_finset_seminorm_boundedproof · cited by 2
- SeminormFamily.filter_eq_iInfproof · cited by 1
- SeminormFamily.basisSets_smulproof · cited by 0
- SeminormFamily.basisSets_smul_leftproof · cited by 0
- SeminormFamily.basisSets_addproof · cited by 0
- SeminormFamily.basisSets_intersectproof · cited by 0