Theorems · Theorem · general topology

Isometry.preimage_closedBall

∀ {α : Type u} {β : Type v} [inst : PseudoMetricSpace α] [inst_1 : PseudoMetricSpace β] {f : α → β},
  Isometry f → ∀ (x : α) (r : ℝ), f ⁻¹' Metric.closedBall (f x) r = Metric.closedBall x r

Defined in

Mathlib.Topology.MetricSpace.Isometry

Cited by

5 results in Mathlib

Foundations

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

Assumes

PseudoMetricSpacePseudoMetricSpace