Theorems · Theorem · general topology
Bornology.IsBounded.subset
∀ {α : Type u_2} {x : Bornology α} {s t : Set α}, Bornology.IsBounded t → s ⊆ t → Bornology.IsBounded s- Defined in
- Mathlib.Topology.Bornology.Basic
- Cited by
- 45 results in Mathlib
- Foundations
- Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Bornology.IsBoundedstatement and proof · cited by 293
- Bornologystatement and proof · cited by 188
- Set.compl_subset_complproof · cited by 50
- Bornology.IsCobounded.supersetproof · cited by 1
Cited by45
Results whose statement or proof uses this declaration.
- Metric.isBounded_ballproof · cited by 15
- Metric.isBounded_iff_subset_closedBallproof · cited by 10
- NormedSpace.isVonNBounded_iffproof · cited by 9
- TotallyBounded.isBoundedproof · cited by 5
- spectrum.isBoundedproof · cited by 4
- AntilipschitzWith.isBounded_of_image2_leftproof · cited by 3
- Metric.isBounded_iff_subset_ballproof · cited by 3
- Bornology.IsBounded.cthickeningproof · cited by 3
- Bornology.IsBounded.prodproof · cited by 3
- exists_contDiff_tsupport_subsetproof · cited by 3
- Bornology.IsBounded.allproof · cited by 2
- Metric.isBounded_of_bddAbove_of_bddBelowproof · cited by 2