Theorems · Theorem · functional analysis
Bornology.IsVonNBounded.vadd
∀ {𝕜 : Type u_1} {E : Type u_3} [inst : NormedField 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
[inst_3 : TopologicalSpace E] [ContinuousSMul 𝕜 E] [ContinuousAdd E] {s : Set E},
Bornology.IsVonNBounded 𝕜 s → ∀ (x : E), Bornology.IsVonNBounded 𝕜 (x +ᵥ s)- Defined in
- Mathlib.Analysis.LocallyConvex.Bounded
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 125 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- HVAdd.hVAddstatement · cited by 1,820
- NormedFieldstatement and proof · cited by 1,084
- ContinuousSMulstatement and proof · cited by 1,016
- ContinuousAddstatement and proof · cited by 777
- Set.vaddSetstatement · cited by 403
- Bornology.IsVonNBoundedstatement and proof · cited by 136
- Set.singleton_vaddproof · cited by 5
- Bornology.IsVonNBounded.addproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Bornology.isVonNBounded_vaddproof · cited by 1