Theorems · Theorem · general topology

Metric.IsCover.image_lipschitz_of_surjective

∀ {X : Type u_1} {Y : Type u_2} [inst : PseudoEMetricSpace X] [inst_1 : PseudoEMetricSpace Y] {f : X → Y} {s : Set Y}
  {N : Set X} {ε K₂ : NNReal},
  Metric.IsCover ε (f ⁻¹' s) N → LipschitzWith K₂ f → Function.Surjective f → Metric.IsCover (K₂ * ε) s (f '' N)

Defined in

Mathlib.Topology.MetricSpace.Cover

Cited by

0 results in Mathlib

Foundations

Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoEMetricSpacePseudoEMetricSpace