reserve r for Real,
  X for set,
  f, g, h for real-valued Function;

theorem
  for T1 being empty TopSpace, T2 being TopSpace for f being Function of
  T1,T2 holds f is continuous
proof
  let T1 be empty TopSpace, T2 being TopSpace;
  let f be Function of T1,T2;
  let A be Subset of T2;
  thus thesis;
end;
