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

theorem
  for X, Y, Z being non empty TopSpace, f being Function of X,Y, g being
  Function of Y,Z st f is open & g is open holds g*f is open
proof
  let X, Y, Z be non empty TopSpace, f be Function of X,Y, g be Function of Y,
  Z such that
A1: f is open and
A2: g is open;
  let A be Subset of X;
  assume A is open;
  then
A3: f.:A is open by A1;
  (g*f).:A = g.:(f.:A) by RELAT_1:126;
  hence thesis by A2,A3;
end;
