reserve i for Integer,
  a, b, r, s for Real;

theorem Th6:
  for X being TopSpace, Y being TopStruct, f being Function of X,Y
  st f is empty holds f is continuous
proof
  let X be TopSpace, Y be TopStruct, f be Function of X,Y such that
A1: f is empty;
  let P being Subset of Y;
  assume P is closed;
  f"P = {}X by A1;
  hence thesis;
end;
