Theorems · Theorem · general topology
uniformity_hasBasis_closed
∀ {α : Type ua} [inst : UniformSpace α], (uniformity α).HasBasis (fun V => V ∈ uniformity α ∧ IsClosed V) id- Defined in
- Mathlib.Topology.UniformSpace.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 81 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.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Filterstatement · cited by 8,121
- Set.ofPredproof · cited by 6,101
- UniformSpacestatement and proof · cited by 2,040
- IsClosedstatement · cited by 1,639
- closureproof · cited by 1,254
- uniformitystatement and proof · cited by 765
- Filter.HasBasisstatement · cited by 604
- SetRelstatement · cited by 581
- subset_closureproof · cited by 309
- Filter.mem_of_supersetproof · cited by 308
- Set.Subset.transproof · cited by 218
Cited by4
Results whose statement or proof uses this declaration.
- mem_uniformity_isClosedproof · cited by 6
- Filter.TotallyBounded.totallyBounded_setOfPred_clusterPtproof · cited by 3
- inseparable_iff_clusterPt_uniformityproof · cited by 2
- uniformity_eq_uniformity_closureproof · cited by 1