Theorems · Theorem · general topology

Metric.preimage_smul_closedBall

∀ {G : Type v} {X : Type w} [inst : PseudoMetricSpace X] [inst_1 : Group G] [inst_2 : MulAction G X]
  [IsIsometricSMul G X] (c : G) (x : X) (r : ℝ),
  (fun x => c • x) ⁻¹' Metric.closedBall x r = Metric.closedBall (c⁻¹ • x) r

Defined in

Mathlib.Topology.MetricSpace.IsometricSMul

Cited by

2 results in Mathlib

Foundations

Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoMetricSpaceGroupMulActionIsIsometricSMul