∀ (R : Type u_1) [inst : CommSemiring R] {A : Type u} [inst_1 : TopologicalSpace A] [inst_2 : Semiring A]
  [inst_3 : Algebra R A] [inst_4 : IsTopologicalSemiring A] [T2Space A] (s : Set A),
  (Algebra.adjoin R s).topologicalClosure ≤ Subalgebra.centralizer R ↑(Subalgebra.centralizer R s)