Theorems · Theorem · general topology

Isometry.diam_image

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

An isometry preserves the diameter in pseudometric spaces.

Defined in

Mathlib.Topology.MetricSpace.Isometry

Cited by

10 results in Mathlib

Foundations

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

Assumes

PseudoMetricSpacePseudoMetricSpace