Theorems · Theorem · general topology
Bornology.IsBounded.bddAbove
∀ {α : Type u_1} {s : Set α} [inst : Bornology α] [inst_1 : Preorder α] [IsOrderBornology α],
Bornology.IsBounded s → BddAbove s- Defined in
- Mathlib.Topology.Order.Bornology
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Bornology.IsBoundedstatement and proof · cited by 293
- Bornologystatement and proof · cited by 188
- IsOrderBornologystatement and proof · cited by 20
- isBounded_iff_bddBelow_bddAboveproof · cited by 7
Cited by7
Results whose statement or proof uses this declaration.
- Real.ediam_eqproof · cited by 4
- Bornology.IsBounded.subset_Icc_sInf_sSupproof · cited by 3
- Real.diam_eqproof · cited by 0
- BoundedContinuousFunction.bddAbove_range_norm_compproof · cited by 0