Theorems · Theorem · general topology
Set.Finite.totallyBounded
∀ {α : Type u} [uniformSpace : UniformSpace α] {s : Set α}, s.Finite → TotallyBounded sA finite set is totally bounded.
- Defined in
- Mathlib.Topology.UniformSpace.Cauchy
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- UniformSpace
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
- UniformSpacestatement and proof · cited by 2,040
- Set.Finitestatement and proof · cited by 1,814
- uniformityproof · cited by 765
- TotallyBoundedstatement · cited by 79
- Set.mem_biUnionproof · cited by 37
- refl_mem_uniformityproof · cited by 15
Cited by3
Results whose statement or proof uses this declaration.
- totallyBounded_emptyproof · cited by 2
- Set.Subsingleton.totallyBoundedproof · cited by 0
- totallyBounded_singletonproof · cited by 0