
theorem Th26:
  for X being non empty TopSpace for Y being monotone-convergence
  non trivial T_0-TopSpace st oContMaps(X, Y) is complete continuous holds
  InclPoset the topology of X is continuous
proof
  let X be non empty TopSpace;
  let Y be monotone-convergence non trivial T_0-TopSpace;
  assume
A1: oContMaps(X, Y) is complete continuous;
  then Sierpinski_Space is_Retract_of Y by Th24,Th25;
  then
A2: oContMaps(X, Sierpinski_Space) is complete continuous by A1,Th23;
  InclPoset the topology of X, oContMaps(X, Sierpinski_Space)
  are_isomorphic by Th6;
  hence thesis by A2,WAYBEL15:9,WAYBEL_1:6;
end;
