Theorems · Theorem · general topology

Dense.extend_exists

∀ {α : Type u_1} {β : Type u_2} [inst : UniformSpace α] [inst_1 : UniformSpace β] {s : Set α} {f : ↑s → β}
  [CompleteSpace β],
  Dense s → UniformContinuous f → ∀ (a : α), ∃ b, Filter.Tendsto f (Filter.comap Subtype.val (nhds a)) (nhds b)

Defined in

Mathlib.Topology.UniformSpace.UniformEmbedding

Cited by

0 results in Mathlib

Foundations

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

Assumes

UniformSpaceUniformSpaceCompleteSpace