
theorem Th4:
  Omega Sierpinski_Space is TopAugmentation of BoolePoset{0}
proof
  set S = the strict Scott TopAugmentation of BoolePoset{0};
A1: the RelStr of S = BoolePoset{0} by YELLOW_9:def 4;
  BoolePoset{0} = InclPoset bool {0} by YELLOW_1:4;
  then
A2: the carrier of BoolePoset{0} = {0,1} by YELLOW14:1,YELLOW_1:1;
  the carrier of Sierpinski_Space = {0,1} & the topology of S = the
  topology of Sierpinski_Space by WAYBEL18:12,def 9;
  then Omega Sierpinski_Space = Omega S by A2,A1,WAYBEL25:13
    .= S by WAYBEL25:15;
  hence thesis;
end;
