for f being Function of I[01],(TOP-REAL 2) st f is continuous & f is one-to-one holds
ex f2 being Function of I[01],(TOP-REAL 2) st
( f2 . 0 = f . 1 & f2 . 1 = f . 0 & rng f2 = rng f & f2 is continuous & f2 is one-to-one )