reserve X for non empty TopSpace;

theorem Th10:
  ex M being Subset of X st M is maximal_T_0
proof
  set A = {}X;
  A is discrete by TEX_2:29;
  then consider M being Subset of X such that
  A c= M and
A1: M is maximal_T_0 by Th9,TSP_1:9;
  take M;
  thus thesis by A1;
end;
