Theorems · Theorem · general topology
TotallyBounded.powerset_hausdorff
∀ {α : Type u_1} [inst : UniformSpace α] {t : Set α}, TotallyBounded t → TotallyBounded (𝒫 t)In the Hausdorff uniformity, the powerset of a totally bounded set is totally bounded.
- Defined in
- Mathlib.Topology.UniformSpace.Closeds
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 71 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.
Cites17
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.iUnion_congr_Propproof · cited by 374
- Filter.basis_setsproof · cited by 105
- TotallyBoundedstatement and proof · cited by 79
- Set.mem_iUnion₂proof · cited by 70
- Set.powersetstatement and proof · cited by 67
- SetRel.imageproof · cited by 49
Cited by3
Results whose statement or proof uses this declaration.
- TopologicalSpace.Closeds.totallyBounded_subsets_of_totallyBoundedproof · cited by 0
- TopologicalSpace.Compacts.totallyBounded_subsets_of_totallyBoundedproof · cited by 0