reserve X for set,
        D for a_partition of X,
        TG for non empty TopologicalGroup;
reserve A for Subset of X;
reserve US for UniformSpace;

theorem
  for US being non empty UniformSpace holds
  the carrier of TopSpace_induced_by(US) = the carrier of US &
  the topology of TopSpace_induced_by(US) = Family_open_set(FMT_induced_by(US))
    by FINTOPO7:def 16;
