Theorems · Theorem · general topology

AntilipschitzWith.ediam_preimage_le

∀ {α : Type u_1} {β : Type u_2} [inst : PseudoEMetricSpace α] [inst_1 : PseudoEMetricSpace β] {K : NNReal} {f : α → β},
  AntilipschitzWith K f → ∀ (s : Set β), Metric.ediam (f ⁻¹' s) ≤ ↑K * Metric.ediam s

Defined in

Mathlib.Topology.MetricSpace.Antilipschitz

Cited by

3 results in Mathlib

Foundations

Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoEMetricSpacePseudoEMetricSpace