(R : Type u_2) →
  [inst : CommRing R] →
    [inst_1 : IsDedekindDomain R] →
      (K : Type u_1) →
        [inst_2 : Field K] →
          [inst_3 : Algebra R K] →
            [inst_4 : IsFractionRing R K] → TopologicalSpace (IsDedekindDomain.FiniteAdeleRing R K)