
theorem
  for a, b being Point of TOP-REAL 2, f being Path of a, b, P being non
  empty compact SubSpace of TOP-REAL 2, g being Function of I[01], P st f is
  one-to-one & g = f & [#]P = rng f holds g is being_homeomorphism
  by COMPTS_1:17,PRE_TOPC:27;
