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
  Family_open_set(FMT_induced_by(US))
    = the set of all O where O is open Subset of FMT_induced_by(US);
