Theorems · Theorem · general topology
Metric.diam_ball
∀ {α : Type u} {x : α} [inst : PseudoMetricSpace α] {r : ℝ}, 0 ≤ r → Metric.diam (Metric.ball x r) ≤ 2 * rThe diameter of a ball of radius r is at most 2 r.
- Defined in
- Mathlib.Topology.MetricSpace.Bounded
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 153 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- PseudoMetricSpacestatement and proof · cited by 1,550
- Metric.ballstatement · cited by 735
- Metric.diamstatement · cited by 74
- Metric.ball_subset_closedBallproof · cited by 46
- Metric.diam_le_of_subset_closedBallproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.measurableSet_range_of_continuous_injectiveproof · cited by 1
- MeasureTheory.SeparableSpace.exists_measurable_partition_diam_leproof · cited by 1
- Metric.diam_ball_eqproof · cited by 0