Theorems · Definition · general topology
Bornology.IsBounded
{α : Type u_2} → [Bornology α] → Set α → PropIsBounded is the predicate that s is bounded relative to the ambient bornology on α.
- Defined in
- Mathlib.Topology.Bornology.Basic
- Cited by
- 293 results in Mathlib
- Foundations
- Depth 6 from the axioms, rests on 19 definitions · uses no axioms
- Assumes
- Bornology
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.complproof · cited by 2,925
- Bornologystatement and proof · cited by 188
- Bornology.IsCoboundedproof · cited by 23
Cited by311
Results whose statement or proof uses this declaration.
- Bornology.IsBounded.subsetstatement and proof · cited by 45
- IsCompact.isBoundedstatement · cited by 29
- Metric.isBounded_closedBallstatement · cited by 19
- isBounded_iff_forall_norm_lestatement and proof · cited by 17
- Metric.isBounded_ballstatement · cited by 15
- Metric.isBounded_iffstatement · cited by 15
- Metric.dist_le_diam_of_memstatement and proof · cited by 14
- Metric.isBounded_iff_subset_closedBallstatement and proof · cited by 10
- Bornology.isBounded_defstatement · cited by 9
- Bornology.IsBounded.bddBelowstatement and proof · cited by 9
- NormedSpace.isVonNBounded_iffstatement · cited by 9
- Bornology.isBounded_compl_iffstatement · cited by 8
Showing the 200 most cited of 311.