
theorem
  for I being 2-element set
  for J being TopSpace-yielding non-Empty ManySortedSet of I
  for i,j being Element of I st i <> j
  holds product J, [: J.i,J.j :] are_homeomorphic
proof
  let I be 2-element set;
  let J be TopSpace-yielding non-Empty ManySortedSet of I;
  let i,j be Element of I;
  assume A1: i <> j;
  reconsider f = <: proj(J,i), proj(J,j) :>
    as Function of product J, [: J.i, J.j :] by BORSUK_1:def 2;
  f is being_homeomorphism by A1,Th74;
  hence thesis by T_0TOPSP:def 1;
end;
