
theorem Th79:
  for I1, I2 being non empty set
  for J1 being TopSpace-yielding non-Empty ManySortedSet of I1
  for J2 being TopSpace-yielding non-Empty ManySortedSet of I2
  for p being Function of I1, I2
  st p is bijective &
    for i being Element of I1 holds J1.i, (J2*p).i are_homeomorphic
  holds product J1, product J2 are_homeomorphic
proof
  let I1, I2 be non empty set;
  let J1 be TopSpace-yielding non-Empty ManySortedSet of I1;
  let J2 be TopSpace-yielding non-Empty ManySortedSet of I2;
  let p be Function of I1, I2;
  assume that
    A1: p is bijective and
    A2: for i being Element of I1 holds J1.i, (J2*p).i are_homeomorphic;
  set H = the ProductHomeo of J1, J2, p;
  H is being_homeomorphism by A1, A2, Th78;
  hence thesis by T_0TOPSP:def 1;
end;
