Theorems · Theorem · general topology

uniformly_extend_spec

∀ {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} (h_e : IsUniformInducing e) (h_dense : DenseRange e) {f : β → γ},
  UniformContinuous f → ∀ [CompleteSpace γ] (a : α), Filter.Tendsto f (Filter.comap e (nhds a)) (nhds (⋯.extend f a))

Defined in

Mathlib.Topology.UniformSpace.UniformEmbedding

Cited by

2 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

UniformSpaceUniformSpaceUniformSpaceCompleteSpace