Theorems · Theorem · general topology

Metric.infEDist_image

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

The infimum edistance is invariant under isometries

Defined in

Mathlib.Topology.MetricSpace.HausdorffDistance

Cited by

7 results in Mathlib

Foundations

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

Assumes

PseudoEMetricSpacePseudoEMetricSpace