
theorem  :: p. 100, Remark 1.4 (iii)
  for T being complete Scott TopLattice holds T is T_0-TopSpace
proof
  let T be complete Scott TopLattice;
  now
    let x,y be Point of T;
    reconsider x9 = x, y9 = y as Element of T;
A1: Cl {x9} = downarrow x9 by Th9;
A2: Cl {y9} = downarrow y9 by Th9;
    assume x <> y;
    hence Cl {x} <> Cl {y} by A1,A2,WAYBEL_0:19;
  end;
  hence thesis by TSP_1:def 5;
end;
