reserve a,b,c for set;
reserve r for Real,
  X for set,
  n for Element of NAT;

theorem
  for X being set holds 1TopSp X = X-DiscreteTop(X)
proof
  let X be set;
  set T = X-DiscreteTop(X);
A1: the carrier of T = X by Def8;
 X c= X;
  then the topology of T = {X} \/ bool X by Th44;
  hence thesis by A1,ZFMISC_1:40;
end;
