Let (X, d) be a compact metric space, and f : X > X such a continuous map that f (a?) :1": x for all :17 E X .Show that there existsaconstant C > 0 such that d (1:, f(:1;)) 2 c for all m E X Hint: Justify that the map 3: |> g (x) :3 (\"3:1 f (55)) is a continuous X } [0, 00) , and apply the minimax theorem