∀ {R : Type u_1} [inst : TopologicalSpace R] [inst_1 : Ring R] [inst_2 : IsTopologicalRing R] (S : Subring R) {a b : R},
  a ∈ S.topologicalClosure.carrier → b ∈ S.topologicalClosure.carrier → a * b ∈ S.topologicalClosure.carrier