Theorems · Theorem · general topology

Isometry.ediam_image

∀ {α : Type u} {β : Type v} [inst : PseudoEMetricSpace α] [inst_1 : PseudoEMetricSpace β] {f : α → β},
  Isometry f → ∀ (s : Set α), Metric.ediam (f '' s) = Metric.ediam s

Isometries preserve the diameter in pseudoemetric spaces.

Defined in

Mathlib.Topology.MetricSpace.Isometry

Cited by

12 results in Mathlib

Foundations

Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoEMetricSpacePseudoEMetricSpace