
theorem
  for S being complete Scott TopLattice holds oContMaps(S,
  Sierpinski_Space) = UPS(S, BoolePoset{0})
proof
  reconsider B1 = BoolePoset{0} as complete LATTICE;
  reconsider OSS = Omega Sierpinski_Space as Scott complete TopAugmentation of
  B1 by Th31,WAYBEL26:4;
  let S be complete Scott TopLattice;
A1: the RelStr of S = the RelStr of S;
  the TopStruct of OSS = the TopStruct of Sierpinski_Space by WAYBEL25:def 2;
  then Omega OSS = OSS by WAYBEL25:13;
  then
A2: the RelStr of OSS = the RelStr of B1 by WAYBEL25:16;
  thus oContMaps(S, Sierpinski_Space) = ContMaps(S, Omega Sierpinski_Space) by
WAYBEL26:def 1
    .= SCMaps(S, OSS) by WAYBEL24:38
    .= UPS(S, OSS) by Th24
    .= UPS(S,BoolePoset{0}) by A1,A2,Th25;
end;
