Theorems · Theorem · general topology

Metric.hausdorffEDist_image

∀ {α : Type u} {β : Type v} [inst : PseudoEMetricSpace α] [inst_1 : PseudoEMetricSpace β] {s t : Set α} {Φ : α → β},
  Isometry Φ → Metric.hausdorffEDist (Φ '' s) (Φ '' t) = Metric.hausdorffEDist s t

The Hausdorff edistance is invariant under isometries.

Defined in

Mathlib.Topology.MetricSpace.HausdorffDistance

Cited by

2 results in Mathlib

Foundations

Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoEMetricSpacePseudoEMetricSpace