Theorems · Theorem · general topology

Isometry.preimage_closedEBall

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

Defined in

Mathlib.Topology.MetricSpace.Isometry

Cited by

3 results in Mathlib

Foundations

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

Assumes

PseudoEMetricSpacePseudoEMetricSpace