∀ {R : Type u_2} [inst : CommRing R] {A : Type u_1} [inst_1 : TopologicalSpace A] [inst_2 : Ring A]
  [inst_3 : Algebra R A] [inst_4 : IsTopologicalRing A] [inst_5 : T2Space A] (s : Subalgebra R A)
  (hs : ∀ (x y : ↥s), x * y = y * x) (a b : ↥s.topologicalClosure), a * b = b * a