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