Theorems · Theorem · general topology
Metric.infEDist_le_hausdorffEDist_of_mem
∀ {α : Type u} [inst : PseudoEMetricSpace α] {x : α} {s t : Set α},
x ∈ s → Metric.infEDist x t ≤ Metric.hausdorffEDist s tThe distance to a set is controlled by the Hausdorff distance.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoEMetricSpace
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 and proof · cited by 53,352
- ENNRealstatement and proof · cited by 9,879
- PseudoEMetricSpacestatement and proof · cited by 1,536
- le_transproof · cited by 985
- le_sup_leftproof · cited by 265
- Metric.infEDiststatement and proof · cited by 147
- Metric.hausdorffEDiststatement · cited by 76
- le_iSup₂proof · cited by 56
- Metric.hausdorffEDist_defproof · cited by 13
Cited by5
Results whose statement or proof uses this declaration.
- Metric.hausdorffEDist_emptyproof · cited by 3
- Metric.exists_edist_lt_of_hausdorffEDist_ltproof · cited by 3
- Metric.hausdorffEDist_triangleproof · cited by 3
- Metric.infDist_le_hausdorffDist_of_memproof · cited by 0
- EMetric.infEdist_le_hausdorffEdist_of_memproof · cited by 0