Theorems · Theorem · general topology

Metric.smul_closedEBall

∀ {G : Type v} {X : Type w} [inst : PseudoEMetricSpace X] [inst_1 : Group G] [inst_2 : MulAction G X]
  [IsIsometricSMul G X] (c : G) (x : X) (r : ENNReal), c • Metric.closedEBall x r = Metric.closedEBall (c • x) r

Defined in

Mathlib.Topology.MetricSpace.IsometricSMul

Cited by

2 results in Mathlib

Foundations

Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoEMetricSpaceGroupMulActionIsIsometricSMul