Theorems · Theorem · general topology
Bornology.isBounded_compl_iff
∀ {α : Type u_2} {x : Bornology α} {s : Set α}, Bornology.IsBounded sᶜ ↔ Bornology.IsCobounded s- Defined in
- Mathlib.Topology.Bornology.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Compl.complstatement and proof · cited by 2,925
- Bornology.IsBoundedstatement · cited by 293
- compl_complproof · cited by 229
- Bornologystatement and proof · cited by 188
- Bornology.coboundedproof · cited by 162
- Bornology.IsCoboundedstatement and proof · cited by 23
- Bornology.isBounded_defproof · cited by 9
- Bornology.isCobounded_defproof · cited by 4
Cited by8
Results whose statement or proof uses this declaration.
- Bornology.IsCobounded.complproof · cited by 1
- Metric.isCobounded_iff_closedBall_compl_subsetproof · cited by 1
- tendsto_const_add_coboundedproof · cited by 1
- tendsto_add_const_coboundedproof · cited by 1
- tendsto_algebraMap_coboundedproof · cited by 0
- isOrderBornology_iff_eq_orderBornologyproof · cited by 0
- Bornology.IsBounded.of_complproof · cited by 0