reserve X for non empty set;

theorem
  for ET being FMT_TopSpace holds ET = TopSpace2FMT FMT2TopSpace ET
  proof
    let ET be FMT_TopSpace;
    FMT2TopSpace ET is strict TopSpace &
    the carrier of FMT2TopSpace ET=the carrier of ET &
    Family_open_set(ET)=the topology of FMT2TopSpace ET by Def10;
    hence thesis by Def9;
  end;
