BoolePoset 1 = InclPoset (bool 1)
by YELLOW_1:4;
then A1:
the carrier of (BoolePoset 1) = {0 ,1}
by YELLOW14:1, YELLOW_1:1;
consider S being strict Scott TopAugmentation of BoolePoset 1;
A2:
the topology of S = the topology of Sierpinski_Space
by WAYBEL18:13;
A3:
RelStr(# the carrier of S,the InternalRel of S #) = BoolePoset 1
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
Omega Sierpinski_Space is Scott
; verum