Theorems · Theorem · general topology
Filter.TotallyBounded.totallyBounded_setOfPred_clusterPt
∀ {α : Type u} [uniformSpace : UniformSpace α] {f : Filter α}, f.TotallyBounded → TotallyBounded {x | ClusterPt x f}- Defined in
- Mathlib.Topology.UniformSpace.Cauchy
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 84 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.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Filterstatement and proof · cited by 8,121
- Set.ofPredstatement and proof · cited by 6,101
- UniformSpacestatement and proof · cited by 2,040
- Set.Finiteproof · cited by 1,814
- IsClosedproof · cited by 1,639
- uniformityproof · cited by 765
- SetRelproof · cited by 581
- IsClosed.closure_eqproof · cited by 139
- ClusterPtstatement and proof · cited by 138
- TotallyBoundedstatement · cited by 79
- SetRel.preimageproof · cited by 56
Cited by3
Results whose statement or proof uses this declaration.
- TotallyBounded.closureproof · cited by 4
- Filter.TotallyBounded.isCompact_setOfPred_clusterPtproof · cited by 1
- Filter.TotallyBounded.totallyBounded_setOf_clusterPtproof · cited by 0