Theorems · Definition · general topology
Metric.sphere
{α : Type u} → [PseudoMetricSpace α] → α → ℝ → Set αsphere x ε is the set of all points y with dist y x = ε
- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 371 results in Mathlib
- Foundations
- Depth 2 from the axioms, rests on 9 definitions · uses no axioms
- Assumes
- PseudoMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- Set.ofPredproof · cited by 6,101
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.distproof · cited by 1,539
Cited by402
Results whose statement or proof uses this declaration.
- Submonoid.unitSphereproof · cited by 85
- Topology.RelCWComplex.cellFrontierproof · cited by 45
- Metric.sphere_subset_closedBallstatement · cited by 24
- circleMap_mem_sphere'statement · cited by 14
- mem_sphere_zero_iff_normstatement · cited by 13
- MeasureTheory.Measure.toSpherestatement · cited by 12
- MeromorphicOn.circleIntegrable_log_normstatement and proof · cited by 11
- isCompact_spherestatement · cited by 11
- norm_eq_of_mem_spherestatement and proof · cited by 11
- stereographicstatement · cited by 10
- Metric.closedBall_sdiff_ballstatement and proof · cited by 10
- Real.circleAverage_congr_spherestatement and proof · cited by 9
Showing the 200 most cited of 402.