Theorems · Theorem · general topology
isBounded_iff_bddBelow_bddAbove
∀ {α : Type u_1} {s : Set α} [inst : Bornology α] [inst_1 : Preorder α] [IsOrderBornology α],
Bornology.IsBounded s ↔ BddBelow s ∧ BddAbove s- Defined in
- Mathlib.Topology.Order.Bornology
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Preorderstatement and proof · cited by 7,952
- BddAbovestatement · cited by 620
- BddBelowstatement · cited by 401
- Bornology.IsBoundedstatement · cited by 293
- Bornologystatement and proof · cited by 188
- IsOrderBornologystatement and proof · cited by 20
- IsOrderBornology.isBounded_iff_bddBelow_bddAboveproof · cited by 2
Cited by7
Results whose statement or proof uses this declaration.
- Bornology.IsBounded.bddBelowproof · cited by 9
- Bornology.IsBounded.bddAboveproof · cited by 7
- IsOrderBornology.atTop_le_coboundedproof · cited by 4
- BddBelow.isBoundedproof · cited by 1
- BddAbove.isBoundedproof · cited by 1
- IsOrderBornology.cobounded_eq_atTopproof · cited by 1
- IsOrderBornology.cobounded_le_atBot_sup_atTopproof · cited by 1