Theorems · Theorem · general topology
Metric.ediam_image_le_iff
∀ {α : Type u_1} {X : Type u_2} [inst : PseudoEMetricSpace X] {d : ENNReal} {f : α → X} {s : Set α},
Metric.ediam (f '' s) ≤ d ↔ ∀ x ∈ s, ∀ y ∈ s, edist (f x) (f y) ≤ d- Defined in
- Mathlib.Topology.EMetricSpace.Diam
- Cited by
- 3 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 and proof · cited by 53,352
- ENNRealstatement and proof · cited by 9,879
- Set.imagestatement and proof · cited by 5,609
- PseudoEMetricSpacestatement and proof · cited by 1,536
- EDist.ediststatement and proof · cited by 735
- Metric.ediamstatement · cited by 159
Cited by3
Results whose statement or proof uses this declaration.
- HolderOnWith.ediam_image_le_of_leproof · cited by 2
- EMetric.diam_image_le_iffproof · cited by 0
- HolderWith.ediam_image_leproof · cited by 0