
theorem Th30:
  for X being monotone-convergence T_0-TopSpace holds Omega X is up-complete
proof
  let X be monotone-convergence T_0-TopSpace;
  for A being non empty directed Subset of Omega X holds ex_sup_of A,Omega
  X by Def4;
  hence thesis by WAYBEL_0:75;
end;
