∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] [inst_2 : Zero β]
  [inst_3 : CompactSpace α],
  Function.LeftInverse (fun f => ↑f) fun f => { toFun := ⇑f, continuous_toFun := ⋯, zero_at_infty' := ⋯ }