theorem Th60:
  P is closed implies MaxADSet(P) = P
proof
  assume P is closed;
  then
A1: Cl P = P by PRE_TOPC:22;
A2: P c= MaxADSet(P) by Th32;
  MaxADSet(P) c= Cl P by Th59;
  hence thesis by A1,A2;
end;
