Theorems · Theorem · general topology
TotallyBounded.closure
∀ {α : Type u} [uniformSpace : UniformSpace α] {s : Set α}, TotallyBounded s → TotallyBounded (closure s)The closure of a totally bounded set is totally bounded.
- Defined in
- Mathlib.Topology.UniformSpace.Cauchy
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 85 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
- closurestatement · cited by 1,254
- TotallyBoundedstatement and proof · cited by 79
- Filter.totallyBounded_principal_iffproof · cited by 6
- closure_eq_cluster_ptsproof · cited by 5
- Filter.TotallyBounded.totallyBounded_setOfPred_clusterPtproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- isClosed_setOfPred_isCompactOperatorproof · cited by 3
- isCompact_closure_interUnionBallsproof · cited by 1
- isCompact_closure_of_totallyBounded_quasiCompleteproof · cited by 1
- totallyBounded_closureproof · cited by 0