Theorems · Theorem · general topology

IsDenseInducing.continuous_extend_of_cauchy

∀ {α : Type u_1} [inst : TopologicalSpace α] {β : Type u_3} [inst_1 : TopologicalSpace β] {γ : Type u_4}
  [inst_2 : UniformSpace γ] [CompleteSpace γ] [T0Space γ] {e : α → β} {f : α → γ} (de : IsDenseInducing e),
  (∀ (b : β), Cauchy (Filter.map f (Filter.comap e (nhds b)))) → Continuous (de.extend f)

Defined in

Mathlib.Topology.UniformSpace.CompleteSeparated

Cited by

1 results in Mathlib

Foundations

Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceUniformSpaceCompleteSpaceT0Space