Theorems · Theorem · general topology
UniformSpace.Completion.uniformity_dist
∀ {α : Type u} [inst : PseudoMetricSpace α],
uniformity (UniformSpace.Completion α) = ⨅ ε, ⨅ (_ : ε > 0), Filter.principal {p | dist p.1 p.2 < ε}- Defined in
- Mathlib.Topology.MetricSpace.Completion
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Filterstatement · cited by 8,121
- Set.ofPredstatement and proof · cited by 6,101
- iInfstatement and proof · cited by 1,690
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement and proof · cited by 1,539
- uniformitystatement and proof · cited by 765
- Filter.principalstatement and proof · cited by 740
- iInf_congr_Propproof · cited by 218
- UniformSpace.Completionstatement and proof · cited by 192
- iInf_subtypeproof · cited by 12
- UniformSpace.Completion.uniformity_dist'proof · cited by 1
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.