Theorems · Theorem · general topology
totallyBounded_interUnionBalls
∀ {α : Type u} [uniformSpace : UniformSpace α] {p : ℕ → Prop} {U : ℕ → SetRel α α},
(uniformity α).HasBasis p U → ∀ (xs : ℕ → α) (u : ℕ → ℕ), TotallyBounded (interUnionBalls xs u U)- Defined in
- Mathlib.Topology.UniformSpace.Cauchy
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 77 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.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coeproof · cited by 8,199
- Set.ofPredproof · cited by 6,101
- Set.imageproof · cited by 5,609
- Set.preimageproof · cited by 4,946
- Set.iUnionproof · cited by 2,483
- UniformSpacestatement and proof · cited by 2,040
- Finset.rangeproof · cited by 1,341
- Set.Iioproof · cited by 1,166
- Finset.imageproof · cited by 910
- uniformitystatement and proof · cited by 765
- Filter.HasBasisstatement and proof · cited by 604
- SetRelstatement and proof · cited by 581
Cited by1
Results whose statement or proof uses this declaration.
- isCompact_closure_interUnionBallsproof · cited by 1