
theorem Th31:
  Omega Sierpinski_Space is Scott
proof
  BoolePoset{0} = InclPoset bool {0} by YELLOW_1:4;
  then
A1: the carrier of BoolePoset{0} = {0,1} by YELLOW14:1,YELLOW_1:1;
  set S = the strict Scott TopAugmentation of BoolePoset{0};
A2: the topology of S = the topology of Sierpinski_Space by WAYBEL18:12;
A3: the RelStr of S = BoolePoset{0} by YELLOW_9:def 4;
  the carrier of Sierpinski_Space = {0,1} by WAYBEL18:def 9;
  then Omega Sierpinski_Space = Omega S by A2,A3,A1,WAYBEL25:13
    .= S by WAYBEL25:15;
  hence thesis;
end;
