BoolePoset 1 = InclPoset (bool 1) by YELLOW_1:4;
then A1: the carrier of (BoolePoset 1) = {0 ,1} by YELLOW14:1, YELLOW_1:1;
A2: the carrier of Sierpinski_Space = {0 ,1} by WAYBEL18:def 9;
consider S being strict Scott TopAugmentation of BoolePoset 1;
( the topology of S = the topology of Sierpinski_Space & RelStr(# the carrier of S,the InternalRel of S #) = BoolePoset 1 ) by WAYBEL18:13, YELLOW_9:def 4;
then Omega Sierpinski_Space = Omega S by A1, A2, WAYBEL25:13
.= S by WAYBEL25:15 ;
hence Omega Sierpinski_Space is Scott ; :: thesis: verum