∀ {ι : Type u_1} {R : Type u_2} {M : Type u_3} [Finite ι] [inst : NontriviallyNormedField R] [CompleteSpace R]
  [inst_2 : AddCommGroup M] [inst_3 : TopologicalSpace M] [IsTopologicalAddGroup M] [T2Space M] [inst_6 : Module R M]
  [ContinuousSMul R M] (B : Module.Basis ι R M), Continuous fun m => ⇑(B.repr m)