Theorems · Theorem · general topology
EMetric.diam_le
Deprecated since 2026-01-04Use Metric.ediam_le instead.
∀ {X : Type u_2} {s : Set X} [inst : PseudoEMetricSpace X] {d : ENNReal},
(∀ x ∈ s, ∀ y ∈ s, edist x y ≤ d) → Metric.ediam s ≤ dAlias of Metric.ediam_le.
If 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
- 0 results in Mathlib
- Foundations
- Depth 150 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 · cited by 53,352
- ENNRealstatement · cited by 9,879
- PseudoEMetricSpacestatement · cited by 1,536
- EDist.ediststatement · cited by 735
- Metric.ediamstatement · cited by 159
- Metric.ediam_leproof · cited by 13
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.