Theorems · Theorem · functional analysis
Bornology.IsVonNBounded.add
∀ {𝕜 : Type u_1} {E : Type u_3} [inst : SeminormedRing 𝕜] [inst_1 : AddZeroClass E] [inst_2 : TopologicalSpace E]
[ContinuousAdd E] [inst_4 : DistribSMul 𝕜 E] {s t : Set E},
Bornology.IsVonNBounded 𝕜 s → Bornology.IsVonNBounded 𝕜 t → Bornology.IsVonNBounded 𝕜 (s + t)- Defined in
- Mathlib.Analysis.LocallyConvex.Bounded
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- nhdsproof · cited by 5,554
- IsOpenproof · cited by 2,400
- AddZeroClassstatement and proof · cited by 1,237
- ContinuousAddstatement and proof · cited by 777
- IsOpen.mem_nhdsproof · cited by 470
- SeminormedRingstatement and proof · cited by 446
- Set.addstatement · cited by 338
- Bornology.IsVonNBoundedstatement and proof · cited by 136
- DistribSMulstatement and proof · cited by 117
- exists_open_nhds_zero_add_subsetproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- Bornology.isVonNBounded_add_of_nonemptyproof · cited by 1
- Bornology.IsVonNBounded.vaddproof · cited by 1
- Bornology.IsVonNBounded.subproof · cited by 0