Theorems · Definition · general topology
TotallyBounded
{α : Type u} → [uniformSpace : UniformSpace α] → Set α → PropA set s is totally bounded if for every entourage d there is a finite
set of points t such that every element of s is d-near to some element of t.
- Defined in
- Mathlib.Topology.UniformSpace.Cauchy
- Cited by
- 79 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- UniformSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
Cited by79
Results whose statement or proof uses this declaration.
- IsCompact.totallyBoundedstatement · cited by 12
- TotallyBounded.subsetstatement and proof · cited by 7
- Filter.HasBasis.totallyBounded_iffstatement · cited by 7
- Filter.totallyBounded_principal_iffstatement · cited by 6
- isCompact_iff_totallyBounded_isCompletestatement and proof · cited by 6
- totallyBounded_Iccstatement · cited by 5
- TotallyBounded.isBoundedstatement and proof · cited by 5
- TotallyBounded.isCompact_of_isClosedstatement and proof · cited by 5
- Metric.totallyBounded_iffstatement · cited by 5
- totallyBounded_iff_subset_finite_iUnion_nhds_zerostatement · cited by 4
- totallyBounded_preimagestatement and proof · cited by 4
- TotallyBounded.closurestatement and proof · cited by 4