
theorem Th32:
  for X,Y being non empty TopSpace holds the carrier of oContMaps(
  X, Y) c= Funcs(the carrier of X, the carrier of Y)
proof
  let X,Y be non empty TopSpace;
  oContMaps(X, Y) is SubRelStr of (Omega Y)|^the carrier of X by WAYBEL24:def 3
;
  then
A1: the carrier of oContMaps(X, Y) c= the carrier of (Omega Y)|^the carrier
  of X by YELLOW_0:def 13;
  the TopStruct of Y = the TopStruct of Omega Y by WAYBEL25:def 2;
  hence thesis by A1,YELLOW_1:28;
end;
