Delta-RELATED FUNCTIONS AND GENERALIZED INVERSE LIMITS

For any continuous single-valued functions f, g : [0, 1]-> 1] we define upper semicontinuous set-valued functions F, G : [0, 1] - by their graphs as the unions of the diagonal Delta and the graphs of set!Lied inverses of f and g respectively. We introduce when two functions are Delta-related and show that if f and g are Delta-related, then the inverse limits lim F and lim G are homeomorphic. lAre also give conditions under which lim G is a quotient space of lim F.