Theorems · Theorem · general topology
Bornology.isBounded_def
∀ {α : Type u_2} {x : Bornology α} {s : Set α}, Bornology.IsBounded s ↔ sᶜ ∈ Bornology.cobounded α- Defined in
- Mathlib.Topology.Bornology.Basic
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Filterstatement · cited by 8,121
- Compl.complstatement · cited by 2,925
- Bornology.IsBoundedstatement · cited by 293
- Bornologystatement and proof · cited by 188
- Bornology.coboundedstatement · cited by 162
Cited by9
Results whose statement or proof uses this declaration.
- Metric.isBounded_iffproof · cited by 15
- Bornology.isBounded_compl_iffproof · cited by 8
- Bornology.isBounded_singletonproof · cited by 6
- Bornology.isBounded_emptyproof · cited by 5
- IsOrderBornology.atTop_le_coboundedproof · cited by 4
- Bornology.cobounded_eq_bot_iffproof · cited by 2
- IsOrderBornology.cobounded_eq_atTopproof · cited by 1
- IsOrderBornology.cobounded_le_atBot_sup_atTopproof · cited by 1
- Bornology.isBounded_ofBounded_iffproof · cited by 1