∀ {R : Type u_5} {A : Type u_4} {M : Type u_1} {N : Type u_2} {ι : Type u_3} [inst : Monoid R] [inst_1 : Semiring A]
  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid N] [inst_4 : TopologicalSpace M] [inst_5 : TopologicalSpace N]
  [inst_6 : Module A M] [inst_7 : Module A N] [inst_8 : DistribMulAction R N] [inst_9 : ContinuousConstSMul R N]
  [inst_10 : SMulCommClass A R N] [inst_11 : ContinuousAdd N] (a : R), a • 0 = 0