Theorems · Theorem · general topology

Isometry.extensionHom_coe

∀ {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] [inst_8 : CompleteSpace β] [inst_9 : T0Space β] {f : α →+* β} (h : Isometry ⇑f)
  (x : α), h.extensionHom ↑x = f x

Defined in

Mathlib.Topology.MetricSpace.Completion

Cited by

2 results in Mathlib

Foundations

Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoMetricSpaceRingIsTopologicalRingIsUniformAddGroupRingPseudoMetricSpaceIsUniformAddGroupIsTopologicalRingCompleteSpaceT0Space