Theorems · Theorem · functional analysis
TotallyBounded.isVonNBounded
∀ (𝕜 : Type u_1) {E : Type u_3} [inst : NormedField 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
[inst_3 : UniformSpace E] [IsUniformAddGroup E] [ContinuousSMul 𝕜 E] {s : Set E},
TotallyBounded s → Bornology.IsVonNBounded 𝕜 s- Defined in
- Mathlib.Analysis.LocallyConvex.Bounded
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites39
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
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- NontriviallyNormedFieldproof · cited by 8,742
- nhdsproof · cited by 5,554
- Norm.normproof · cited by 5,413
- Filter.Tendstoproof · cited by 3,814
- Set.iUnionproof · cited by 2,483
- zero_addproof · cited by 2,366
- UniformSpacestatement and proof · cited by 2,040
- HVAdd.hVAddproof · cited by 1,820
- Set.Finiteproof · cited by 1,814
Cited by4
Results whose statement or proof uses this declaration.
- FiniteDimensional.of_totallyBounded_nhds_zeroproof · cited by 3
- IsCompact.isVonNBoundedproof · cited by 1
- Filter.Tendsto.isVonNBounded_rangeproof · cited by 1
- isCompact_closure_of_totallyBounded_quasiCompleteproof · cited by 1