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,
      S being Subset of FMT_induced_by(US) holds
  S in Family_open_set(FMT_induced_by(US)) iff for x being Element of US st
  x in S holds S in Neighborhood x by Th8,Th9;
