Theorems · Theorem · functional analysis
Bornology.IsVonNBounded.neg
∀ {𝕜 : Type u_1} {E : Type u_3} [inst : SeminormedRing 𝕜] [inst_1 : AddGroup E] [inst_2 : TopologicalSpace E]
[IsTopologicalAddGroup E] [inst_4 : DistribMulAction 𝕜 E] {s : Set E},
Bornology.IsVonNBounded 𝕜 s → Bornology.IsVonNBounded 𝕜 (-s)- Defined in
- Mathlib.Analysis.LocallyConvex.Bounded
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 75 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
- nhdsproof · cited by 5,554
- AddGroupstatement and proof · cited by 4,410
- IsTopologicalAddGroupstatement and proof · cited by 1,394
- neg_negproof · cited by 960
- DistribMulActionstatement and proof · cited by 584
- SeminormedRingstatement and proof · cited by 446
- Set.negstatement · cited by 168
- Bornology.IsVonNBoundedstatement and proof · cited by 136
- Absorbsproof · cited by 59
- neg_mem_nhds_zeroproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- Bornology.isVonNBounded_negproof · cited by 1
- Bornology.IsVonNBounded.subproof · cited by 0