Theorems · Theorem · general topology
Bornology.IsBounded.subset_Icc_sInf_sSup
∀ {α : Type u_1} [inst : Bornology α] [inst_1 : ConditionallyCompleteLattice α] [IsOrderBornology α] {s : Set α},
Bornology.IsBounded s → s ⊆ Set.Icc (sInf s) (sSup s)- Defined in
- Mathlib.Topology.Order.Bornology
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Set.Iccstatement · cited by 1,702
- SupSet.sSupstatement · cited by 954
- InfSet.sInfstatement · cited by 935
- ConditionallyCompleteLatticestatement and proof · cited by 364
- Bornology.IsBoundedstatement and proof · cited by 293
- Bornologystatement and proof · cited by 188
- IsOrderBornologystatement and proof · cited by 20
- Bornology.IsBounded.bddBelowproof · cited by 9
- Bornology.IsBounded.bddAboveproof · cited by 7
- subset_Icc_csInf_csSupproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- Real.ediam_eqproof · cited by 4
- locallyIntegrableOn_mul_sum_Iccproof · cited by 2
- Real.volume_le_diamproof · cited by 1