Theorems · Definition · general topology

Isometry.mapRingHom

{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] →
                [inst_6 : IsUniformAddGroup β] →
                  [inst_7 : IsTopologicalRing β] →
                    {f : α →+* β} → Isometry ⇑f → UniformSpace.Completion α →+* UniformSpace.Completion β

The lift of an isometry to completions.

Defined in

Mathlib.Topology.MetricSpace.Completion

Cited by

3 results in Mathlib

Foundations

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

Assumes

PseudoMetricSpaceRingIsTopologicalRingIsUniformAddGroupRingPseudoMetricSpaceIsUniformAddGroupIsTopologicalRing