Theorems · Theorem · general topology
TotallyBounded.subset
∀ {α : Type u} [uniformSpace : UniformSpace α] {s₁ s₂ : Set α}, s₁ ⊆ s₂ → TotallyBounded s₂ → TotallyBounded s₁- Defined in
- Mathlib.Topology.UniformSpace.Cauchy
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- UniformSpace
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
- Set.ofPredproof · cited by 6,101
- Set.iUnionproof · cited by 2,483
- UniformSpacestatement and proof · cited by 2,040
- Set.Finiteproof · cited by 1,814
- uniformityproof · cited by 765
- Set.Subset.transproof · cited by 218
- TotallyBoundedstatement and proof · cited by 79
Cited by7
Results whose statement or proof uses this declaration.
- totallyBounded_preimageproof · cited by 4
- totallyBounded_Iooproof · cited by 2
- totallyBounded_Icoproof · cited by 1
- totallyBounded_Iocproof · cited by 1
- Metric.exists_finite_isCover_of_isCompact_closureproof · cited by 1
- totallyBounded_closureproof · cited by 0
- totallyBounded_convexHullproof · cited by 0