Theorems · Theorem · general topology
Metric.ediam_mono
∀ {X : Type u_2} {s t : Set X} [inst : PseudoEMetricSpace X], s ⊆ t → Metric.ediam s ≤ Metric.ediam tThe extended diameter is monotonous with respect to inclusion
- Defined in
- Mathlib.Topology.EMetricSpace.Diam
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 151 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 · cited by 9,879
- PseudoEMetricSpacestatement and proof · cited by 1,536
- Metric.ediamstatement · cited by 159
- Metric.edist_le_ediam_of_memproof · cited by 20
- Metric.ediam_leproof · cited by 13
Cited by14
Results whose statement or proof uses this declaration.
- Metric.diam_monoproof · cited by 7
- Metric.ediam_closureproof · cited by 5
- MeasureTheory.OuterMeasure.isometry_comap_mkMetricproof · cited by 3
- IsCompact.uniform_oscillationWithinproof · cited by 2
- Metric.diam_unionproof · cited by 2
- convexHull_ediamproof · cited by 2
- Metric.ediam_eball_leproof · cited by 2
- Real.ediam_Icoproof · cited by 1
- Real.ediam_Iocproof · cited by 1
- AntilipschitzWith.le_mul_ediam_imageproof · cited by 1
- Metric.diam_cthickening_leproof · cited by 1
- HolderOnWith.ediam_image_inter_le_of_leproof · cited by 1