∀ {X : Type u_2} {Y : Type u_3} {Z : Type u_4} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
  [inst_2 : TopologicalSpace Z] {f : X → C(Y, Z)},
  Continuous f ↔ ∀ (K : Set Y), IsCompact K → ∀ (U : Set Z), IsOpen U → IsOpen {x | Set.MapsTo (⇑(f x)) K U}