reserve X for non empty set;

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