Theorems · Definition · general topology
Metric.diam
{α : Type u} → [PseudoMetricSpace α] → Set α → ℝThe diameter of a set in a metric space. To get controllable behavior even when the diameter
should be infinite, we express it in terms of the ediam
- Defined in
- Mathlib.Topology.MetricSpace.Bounded
- Cited by
- 74 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.ediamproof · cited by 159
Cited by74
Results whose statement or proof uses this declaration.
- Metric.dist_le_diam_of_memstatement · cited by 14
- Isometry.diam_imagestatement and proof · cited by 10
- Metric.diam_monostatement · cited by 7
- Metric.diam_le_of_forall_dist_lestatement · cited by 5
- Metric.diam_nonnegstatement · cited by 5
- Metric.isBounded_iff_ediam_ne_topproof · cited by 5
- Isometry.diam_rangestatement and proof · cited by 5
- Metric.diam_closedBallstatement · cited by 4
- Metric.diam_ballstatement · cited by 3
- Metric.diam_singletonstatement · cited by 3
- Metric.diam_emptystatement · cited by 3
- Metric.diam_sphere_eqstatement · cited by 2