Theorems · Theorem · general topology
UniformSpace.hausdorff.isClosed_setOfPred_totallyBounded
∀ {α : Type u_1} [inst : UniformSpace α], IsClosed {s | TotallyBounded s}- Defined in
- Mathlib.Topology.UniformSpace.Closeds
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 70 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.
Cites29
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.ofPredstatement and proof · cited by 6,101
- Set.preimageproof · cited by 4,946
- Set.iUnionproof · cited by 2,483
- le_reflproof · cited by 2,061
- UniformSpacestatement and proof · cited by 2,040
- Set.Finiteproof · cited by 1,814
- IsClosedstatement · cited by 1,639
- uniformityproof · cited by 765
- le_imp_le_of_le_of_leproof · cited by 576
- Filter.comapproof · cited by 546
- Filter.Frequentlyproof · cited by 414
Cited by2
Results whose statement or proof uses this declaration.
- TopologicalSpace.Closeds.isClosed_setOfPred_totallyBoundedproof · cited by 2
- UniformSpace.hausdorff.isClosed_setOf_totallyBoundedproof · cited by 0