reserve Y for TopStruct;
reserve X for non empty TopSpace;
reserve X for almost_discrete non empty TopSpace;

theorem Th57:
  for A being Subset of X st A is maximal_discrete holds union {Cl
  {a} where a is Point of X : a in A} = the carrier of X
proof
  let A be Subset of X;
  assume A is maximal_discrete;
  then A is dense by Th56;
  then Cl A = the carrier of X by TOPS_3:def 2;
  hence thesis by Th48;
end;
