∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {i : α → β}
  [inst_2 : TopologicalSpace γ] (di : IsDenseInducing i) (f : α → γ) (b : β),
  di.extend f b = limUnder (Filter.comap i (nhds b)) f