∀ {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] [T2Space γ] (di : IsDenseInducing i) {f : α → γ} {a : α} (c : γ),
  Filter.Tendsto f (nhds a) (nhds c) → di.extend f (i a) = f a