Theorems · Definition · general topology
Metric.infDist
{α : Type u} → [PseudoMetricSpace α] → α → Set α → ℝThe minimal distance of a point to a set
- Cited by
- 68 results in Mathlib
- Foundations
- Depth 148 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement · cited by 25,697
- PseudoMetricSpacestatement and proof · cited by 1,550
- ENNReal.toRealproof · cited by 859
- Metric.infEDistproof · cited by 147
Cited by70
Results whose statement or proof uses this declaration.
- Metric.infDist_le_dist_of_memstatement and proof · cited by 13
- EuclideanGeometry.dist_orthogonalProjection_eq_infDiststatement · cited by 5
- Metric.mem_closure_iff_infDist_zerostatement · cited by 5
- Metric.infDist_eq_iInfstatement · cited by 4
- Metric.infDist_lt_iffstatement · cited by 4
- IsClosed.notMem_iff_infDist_posstatement and proof · cited by 4
- Metric.infDist_imagestatement · cited by 3
- Metric.infDist_nonnegstatement · cited by 3
- IsClosed.mem_iff_infDist_zerostatement · cited by 3
- Metric.le_infDiststatement · cited by 3
- riesz_lemmaproof · cited by 2
- Metric.mem_thickening_iff_infDist_ltstatement · cited by 2