
theorem Th19:
  for X being non empty TopSpace for Z being monotone-convergence
  T_0-TopSpace for Y being non empty SubSpace of Z st Y is_a_retract_of Z holds
  oContMaps(X, Y) is_a_retract_of oContMaps(X, Z)
proof
  let X be non empty TopSpace;
  let Z be monotone-convergence T_0-TopSpace;
  let Y be non empty SubSpace of Z;
  given f being continuous Function of Z,Y such that
A1: f is being_a_retraction;
  take oContMaps(X, f);
  thus thesis by A1,Th18;
end;
