
theorem Th1:
  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, Omega Y
proof
  let X,Y be non empty TopSpace;
  let a be set;
  hereby
    assume a is Element of oContMaps(X,Y);
    then ex f being Function of X, Omega Y st a = f & f is continuous by
WAYBEL24:def 3;
    hence a is continuous Function of X, Omega Y;
  end;
  assume a is continuous Function of X, Omega Y;
  hence thesis by WAYBEL24:def 3;
end;
