Theorems · Theorem · functional analysis
SeminormFamily.withSeminorms_of_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]
[t : TopologicalSpace E] [IsTopologicalAddGroup E] (p : SeminormFamily 𝕜 E ι),
(nhds 0).HasBasis (fun s => s ∈ p.basisSets) id → WithSeminorms p- Cited by
- 1 results in Mathlib
- Foundations
- Depth 135 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
- nhdsstatement and proof · cited by 5,554
- IsTopologicalAddGroupstatement and proof · cited by 1,394
- NormedFieldstatement and proof · cited by 1,084
- Filter.HasBasisstatement and proof · cited by 604
- WithSeminormsstatement · cited by 69
- SeminormFamilystatement and proof · cited by 68
- AddGroupFilterBasis.toFilterBasisproof · cited by 32
- SeminormFamily.basisSetsstatement and proof · cited by 22
Cited by1
Results whose statement or proof uses this declaration.
- with_gaugeSeminormFamilyproof · cited by 0