Theorems · Theorem · general topology
LipschitzWith.ediam_image_le
∀ {α : Type u} {β : Type v} [inst : PseudoEMetricSpace α] [inst_1 : PseudoEMetricSpace β] {K : NNReal} {f : α → β},
LipschitzWith K f → ∀ (s : Set α), Metric.ediam (f '' s) ≤ ↑K * Metric.ediam s- Defined in
- Mathlib.Topology.EMetricSpace.Lipschitz
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Set.imagestatement and proof · cited by 5,609
- NNRealstatement and proof · cited by 4,310
- PseudoEMetricSpacestatement and proof · cited by 1,536
- ENNReal.ofNNRealstatement · cited by 1,279
- LipschitzWithstatement and proof · cited by 316
- Metric.ediamstatement · cited by 159
- Metric.edist_le_ediam_of_memproof · cited by 20
- Metric.ediam_leproof · cited by 13
- LipschitzWith.edist_le_mul_of_leproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- Dilation.ediam_imageproof · cited by 2
- Real.volume_pi_le_diam_powproof · cited by 1
- ediam_smul_leproof · cited by 1
- ediam_smul₀proof · cited by 1