let T be TopSpace; :: thesis: {} T is scattered
{} T is scattered

proof

assume not {} T is scattered ; :: thesis: contradiction
then consider B being Subset of T such that
A1: ( not B is empty & B c= {} T & B is dense-in-itself ) by Def11;
thus contradiction by A1; :: thesis: verum

end;

hence {} T is scattered ; :: thesis: verum