
theorem Th2:
  for X,Y being non empty TopSpace for a being set holds a is
  Element of oContMaps(X, Y) iff a is continuous Function of X, Y
proof
  let X,Y be non empty TopSpace;
  let a be set;
A1: the TopStruct of Omega Y = the TopStruct of Y & the TopStruct of X = the
  TopStruct of X by WAYBEL25:def 2;
  hereby
    assume a is Element of oContMaps(X,Y);
    then a is continuous Function of X, Omega Y by Th1;
    hence a is continuous Function of X, Y by A1,YELLOW12:36;
  end;
  assume a is continuous Function of X, Y;
  then a is continuous Function of X, Omega Y by A1,YELLOW12:36;
  hence thesis by Th1;
end;
