∀ (X : Type u_1) [inst : TopologicalSpace X] (Y : Type u_2) [inst_1 : DiscreteTopology X] [inst_2 : TopologicalSpace Y]
  [T2Space Y] [Infinite X] (f : C(OnePoint X, Y)),
  (fun f =>
        {
          toFun := fun x =>
            match x with
            | none => Classical.choose ⋯
            | some x => ↑f x,
          continuous_toFun := ⋯ })
      ((fun f => ⟨fun x => f ↑x, ⋯⟩) f) =
    f