
theorem Th7:
  for X being non empty TopSpace for Y being monotone-convergence
  T_0-TopSpace holds oContMaps(X, Y) is up-complete
proof
  let X be non empty TopSpace;
  let Y be monotone-convergence T_0-TopSpace;
  ContMaps(X, Omega Y) is directed-sups-inheriting full SubRelStr of (
  Omega Y) |^ the carrier of X by WAYBEL24:def 3,WAYBEL25:43;
  hence thesis by YELLOW16:5;
end;
