Theorems · Theorem · functional analysis
asymptoticCone_subset_singleton_of_bounded
∀ {V : Type u_1} {P : Type u_2} [inst : NormedAddCommGroup V] [inst_1 : NormedSpace ℝ V] [inst_2 : MetricSpace P]
[inst_3 : NormedAddTorsor V P] {s : Set P}, Bornology.IsBounded s → asymptoticCone ℝ s ⊆ {0}- Cited by
- 1 results in Mathlib
- Foundations
- Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Set.ofPredproof · cited by 6,101
- MetricSpacestatement and proof · cited by 1,684
- NormedAddTorsorstatement and proof · cited by 1,325
- Bornology.IsBoundedstatement and proof · cited by 293
- asymptoticConestatement and proof · cited by 26
- AffineSpace.asymptoticNhds_le_coboundedproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- isBounded_iff_asymptoticCone_subset_singletonproof · cited by 1