Theorems · Definition · general topology
uniformity
(α : Type u) → [UniformSpace α] → Filter (α × α)
The uniformity is a filter on α × α (inferred from an ambient uniform space structure on α).
- Defined in
- Mathlib.Topology.UniformSpace.Defs
- Cited by
- 765 results in Mathlib
- Foundations
- Depth 2 from the axioms, rests on 5 definitions · uses no axioms
- Assumes
- UniformSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Filterstatement · cited by 8,121
- UniformSpacestatement and proof · cited by 2,040
- UniformSpace.uniformityproof · cited by 5
Cited by826
Results whose statement or proof uses this declaration.
- UniformContinuousproof · cited by 410
- TendstoUniformlyOnproof · cited by 129
- Cauchyproof · cited by 115
- TendstoLocallyUniformlyOnproof · cited by 84
- TotallyBoundedproof · cited by 79
- TendstoUniformlyproof · cited by 75
- UniformSpace.comapproof · cited by 61
- TendstoLocallyUniformlyproof · cited by 59
- TendstoUniformlyOnFilterproof · cited by 50
- UniformContinuousOnproof · cited by 47
- EquicontinuousAtproof · cited by 39
- UniformEquicontinuousproof · cited by 35
Showing the 200 most cited of 826.