Topological Conjugacies of Piecewise Monotone Interval Maps

this paper we consider the family M of functions which are piecewise monotone but not necessarily continuous. Particularly, f : [0; 1] ! [0; 1] belongs in the family M if there exists a partition 0 = a 0 ! a 1 ! : : : ! a r = 1, (r 2) of [0,1] such that f j(a i\Gamma1 ; a i ) (i = 1; 2; : : : ; r