Theorems · Definition · general topology
Metric.AreSeparated
{X : Type u_1} → [PseudoEMetricSpace X] → Set X → Set X → PropTwo sets in an (extended) metric space are called metric separated if the (extended) distance
between x ∈ s and y ∈ t is bounded from below by a positive constant.
- Cited by
- 23 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.
Cites4
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
- ENNRealproof · cited by 9,879
- PseudoEMetricSpacestatement and proof · cited by 1,536
- EDist.edistproof · cited by 735
Cited by24
Results whose statement or proof uses this declaration.
- Metric.AreSeparated.symmstatement and proof · cited by 4
- MeasureTheory.OuterMeasure.IsMetricproof · cited by 4
- Metric.AreSeparated.finite_iUnion_left_iffstatement and proof · cited by 3
- Metric.AreSeparated.monostatement and proof · cited by 3
- Metric.AreSeparated.commstatement · cited by 2
- Metric.AreSeparated.union_leftstatement and proof · cited by 2
- Metric.AreSeparated.union_left_iffstatement and proof · cited by 2
- MeasureTheory.OuterMeasure.IsMetric.borel_le_caratheodoryproof · cited by 1
- MeasureTheory.OuterMeasure.IsMetric.finset_iUnion_of_pairwise_separatedstatement and proof · cited by 1
- Metric.AreSeparated.disjointstatement and proof · cited by 1
- Metric.AreSeparated.empty_leftstatement · cited by 1
- Metric.AreSeparated.finite_iUnion_right_iffstatement · cited by 1