Theorems · Definition · general topology
Metric.IsSeparated
{X : Type u_1} → [PseudoEMetricSpace X] → ENNReal → Set X → PropA set s is ε-separated if the extended distance between any two distinct
elements is strictly greater than ε.
- Cited by
- 28 results in Mathlib
- Foundations
- Depth 147 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.
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
- ENNRealstatement and proof · cited by 9,879
- PseudoEMetricSpacestatement and proof · cited by 1,536
- EDist.edistproof · cited by 735
- Set.Pairwiseproof · cited by 321
Cited by34
Results whose statement or proof uses this declaration.
- Metric.packingNumberproof · cited by 14
- Delone.DeloneSet.extproof · cited by 6
- Metric.packingNumber_le_encard_selfproof · cited by 2
- Metric.packingNumber_two_mul_le_externalCoveringNumberproof · cited by 2
- Delone.DeloneSet.mk.congr_simpstatement and proof · cited by 2
- Metric.IsSeparated.of_subsingletonstatement · cited by 1
- Metric.isCover_maximalSeparatedSetproof · cited by 1
- Delone.DeloneSet.mk.injstatement and proof · cited by 1
- Delone.DeloneSet.mk.noConfusionstatement and proof · cited by 1
- Metric.encard_le_of_isSeparatedstatement and proof · cited by 1
- Metric.isSeparated_insertstatement · cited by 1
- Metric.isSeparated_insert_of_notMemstatement · cited by 1