Theorems · Theorem · general topology
Metric.diam_nonneg
∀ {α : Type u} {s : Set α} [inst : PseudoMetricSpace α], 0 ≤ Metric.diam sThe diameter of a set is always nonnegative
- Defined in
- Mathlib.Topology.MetricSpace.Bounded
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 149 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.toReal_nonnegproof · cited by 86
- Metric.diamstatement · cited by 74
Cited by5
Results whose statement or proof uses this declaration.
- exists_nat_nat_continuous_surjective_of_completeSpaceproof · cited by 1
- Metric.hausdorffDist_le_diamproof · cited by 0
- Metric.diam_ball_eqproof · cited by 0
- Metric.diam_thickening_leproof · cited by 0
- LipschitzWith.diam_image_leproof · cited by 0