Theorems · Theorem · general topology

UniformSpace.Completion.extension_map

∀ {α : Type u_1} [inst : UniformSpace α] {β : Type u_2} [inst_1 : UniformSpace β] {γ : Type u_3}
  [inst_2 : UniformSpace γ] [CompleteSpace γ] [T0Space γ] {f : β → γ} {g : α → β},
  UniformContinuous f →
    UniformContinuous g →
      UniformSpace.Completion.extension f ∘ UniformSpace.Completion.map g = UniformSpace.Completion.extension (f ∘ g)

Defined in

Mathlib.Topology.UniformSpace.Completion

Cited by

1 results in Mathlib

Foundations

Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

UniformSpaceUniformSpaceUniformSpaceCompleteSpaceT0Space