Theorems · Definition · general topology

Isometry.extensionHom

{α : Type u} →
  {β : Type v} →
    [inst : PseudoMetricSpace α] →
      [inst_1 : Ring α] →
        [inst_2 : IsTopologicalRing α] →
          [inst_3 : IsUniformAddGroup α] →
            [inst_4 : Ring β] →
              [inst_5 : PseudoMetricSpace β] →
                [IsUniformAddGroup β] →
                  [IsTopologicalRing β] →
                    [CompleteSpace β] → [T0Space β] → {f : α →+* β} → Isometry ⇑f → UniformSpace.Completion α →+* β

The extension of an isometry to the completion of the domain.

Defined in

Mathlib.Topology.MetricSpace.Completion

Cited by

1 results in Mathlib

Foundations

Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoMetricSpaceRingIsTopologicalRingIsUniformAddGroupRingPseudoMetricSpaceIsUniformAddGroupIsTopologicalRingCompleteSpaceT0Space