Theorems · Theorem · general topology
Metric.infDist_singleton
∀ {α : Type u} [inst : PseudoMetricSpace α] {x y : α}, Metric.infDist x {y} = dist x yThe minimal distance to a singleton is the distance to the unique point in this singleton.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 149 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement · cited by 25,697
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement · cited by 1,539
- ENNReal.toRealproof · cited by 859
- EDist.edistproof · cited by 735
- Metric.infDiststatement · cited by 68
- dist_edistproof · cited by 21
- Metric.infEDist_singletonproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- AddCircle.norm_eq_of_zeroproof · cited by 2