∀ {E : Type u_1} {F : Type u_2} [inst : AddCommGroup E] [inst_1 : Module ℝ E] [inst_2 : TopologicalSpace E] [T2Space E]
  [IsTopologicalAddGroup E] [ContinuousSMul ℝ E] [LocallyConvexSpace ℝ E] {s : Set E} [inst_7 : AddCommGroup F]
  [inst_8 : Module ℝ F] [inst_9 : TopologicalSpace F] [T1Space F] (f : E →ᴬ[ℝ] F),
  IsCompact s → Set.SurjOn (⇑f) (Set.extremePoints ℝ s) (Set.extremePoints ℝ (⇑f '' s))