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