Theorems · Definition · general topology

IsometryEquiv.constVAdd

{G : Type v} →
  {X : Type w} →
    [inst : PseudoEMetricSpace X] →
      [inst_1 : AddGroup G] → [inst_2 : AddAction G X] → [IsIsometricVAdd G X] → G → X ≃ᵢ X

If an additive group G acts on X by isometries, then IsometryEquiv.constVAdd is the isometry of X given by addition of a constant element of the group.

Defined in

Mathlib.Topology.MetricSpace.IsometricSMul

Cited by

8 results in Mathlib

Foundations

Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoEMetricSpaceAddGroupAddActionIsIsometricVAdd