∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : CompactSpace α] [inst_2 : PseudoMetricSpace β]
  {R : Type u_4} [inst_3 : Zero R] [inst_4 : Zero β] [inst_5 : PseudoMetricSpace R] [inst_6 : SMul R β]
  [inst_7 : IsBoundedSMul R β], IsBoundedSMul R C(α, β)