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