Theorems · Theorem · functional analysis
WithSeminorms.hasBasis
∀ {𝕜 : Type u_2} {E : Type u_6} {ι : Type u_9} [inst : NormedField 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
[inst_3 : TopologicalSpace E] {p : SeminormFamily 𝕜 E ι},
WithSeminorms p → (nhds 0).HasBasis (fun s => s ∈ p.basisSets) id- Cited by
- 5 results in Mathlib
- Foundations
- Depth 134 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Filterproof · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- NormedFieldstatement and proof · cited by 1,084
- Filter.HasBasisstatement and proof · cited by 604
- WithSeminormsstatement and proof · cited by 69
- SeminormFamilystatement and proof · cited by 68
- SeminormFamily.basisSetsstatement and proof · cited by 22
- SeminormFamily.moduleFilterBasisproof · cited by 10
Cited by5
Results whose statement or proof uses this declaration.
- Seminorm.bound_of_continuousproof · cited by 2
- WithSeminorms.hasBasis_zero_ballproof · cited by 2
- WithSeminorms.isVonNBounded_iff_finset_seminorm_boundedproof · cited by 2
- LinearMap.hasBasis_weakBilinproof · cited by 0
- ContinuousLinearMapWOT.hasBasis_seminormsproof · cited by 0