Theorems · Theorem · general topology
nhds_comap_dist
∀ {α : Type u} [inst : PseudoMetricSpace α] (a : α), Filter.comap (fun x => dist x a) (nhds 0) = nhds a- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 117 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Filterstatement · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- UniformSpaceproof · cited by 2,040
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement and proof · cited by 1,539
- Filter.comapstatement and proof · cited by 546
- dist_commproof · cited by 188
- Filter.comap_comapproof · cited by 69
- nhds_eq_comap_uniformityproof · cited by 19
- Metric.uniformity_eq_comap_nhds_zeroproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- tendsto_iff_dist_tendsto_zeroproof · cited by 16
- comap_norm_nhds_zeroproof · cited by 7
- comap_norm_nhds_oneproof · cited by 1