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