Theorems · Theorem · general topology
Metric.ediam_le
∀ {X : Type u_2} {s : Set X} [inst : PseudoEMetricSpace X] {d : ENNReal},
(∀ x ∈ s, ∀ y ∈ s, edist x y ≤ d) → Metric.ediam s ≤ dIf the distance between any two points in a set is bounded by some constant, this constant bounds the diameter.
- Defined in
- Mathlib.Topology.EMetricSpace.Diam
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 149 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.
Cites6
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.ediststatement and proof · cited by 735
- Metric.ediamstatement · cited by 159
- Metric.ediam_le_iffproof · cited by 4
Cited by13
Results whose statement or proof uses this declaration.
- Metric.ediam_monoproof · cited by 14
- Metric.ediam_subsingletonproof · cited by 6
- Metric.ediam_closureproof · cited by 5
- LipschitzWith.ediam_image_leproof · cited by 4
- Metric.ediam_union_le_add_edistproof · cited by 3
- Metric.ediam_le_of_forall_dist_leproof · cited by 3
- AntilipschitzWith.ediam_preimage_leproof · cited by 3
- Metric.ediam_pi_le_of_leproof · cited by 3
- Metric.ediam_closedEBall_leproof · cited by 2
- convexHull_ediamproof · cited by 2
- Metric.ediam_cthickening_leproof · cited by 2
- EMetric.cauchySeq_iff_le_tendsto_0proof · cited by 0