Theorems · Theorem · general topology
Metric.uniformity_eq_comap_nhds_zero
∀ {α : Type u} [inst : PseudoMetricSpace α], uniformity α = Filter.comap (fun p => dist p.1 p.2) (nhds 0)- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 116 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.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Realstatement and proof · cited by 25,697
- Filterstatement · cited by 8,121
- nhdsstatement · cited by 5,554
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement and proof · cited by 1,539
- uniformitystatement · cited by 765
- Filter.comapstatement · cited by 546
- Filter.HasBasis.mem_iffproof · cited by 193
- Filter.HasBasis.comapproof · cited by 89
- Filter.extproof · cited by 60
- Metric.nhds_basis_ballproof · cited by 41
Cited by4
Results whose statement or proof uses this declaration.
- Seminorm.uniformContinuous_of_continuousAt_zeroproof · cited by 5
- nhds_comap_distproof · cited by 3
- tendsto_uniformity_iff_dist_tendsto_zeroproof · cited by 2
- cauchySeq_iff_tendsto_dist_atTop_0proof · cited by 0