Theorems · Theorem · general topology

Metric.preimage_vadd_closedEBall

∀ {G : Type v} {X : Type w} [inst : PseudoEMetricSpace X] [inst_1 : AddGroup G] [inst_2 : AddAction G X]
  [IsIsometricVAdd G X] (c : G) (x : X) (r : ENNReal),
  (fun x => c +ᵥ x) ⁻¹' Metric.closedEBall x r = Metric.closedEBall (-c +ᵥ x) r

Defined in

Mathlib.Topology.MetricSpace.IsometricSMul

Cited by

3 results in Mathlib

Foundations

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

Assumes

PseudoEMetricSpaceAddGroupAddActionIsIsometricVAdd