Theorems · Theorem · general topology

uniformly_extend_exists

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : UniformSpace α] [inst_1 : UniformSpace β]
  [inst_2 : UniformSpace γ] {e : β → α},
  IsUniformInducing e →
    DenseRange e →
      ∀ {f : β → γ},
        UniformContinuous f → ∀ [CompleteSpace γ] (a : α), ∃ c, Filter.Tendsto f (Filter.comap e (nhds a)) (nhds c)

Defined in

Mathlib.Topology.UniformSpace.UniformEmbedding

Cited by

3 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

UniformSpaceUniformSpaceUniformSpaceCompleteSpace