An Arc As The Inverse Limit Of A Single Bonding Map Of Type N On[0,1]

Let I = [0, 1] and c1,c2 ε (0. 1) with c1 < c2,f: I → I be acontinuous map satisfying: fI[0. c1] and fI[c2, 1] are both strictly increasingallcl fI[c1. c2] is strictly decreasing. Let and min(B\{6}). Then the inverse limit (I. f) is an arc if and only if one of thefollo\x.ing three conditions holds:1. If then f has a single fixed point.a periocl two orbit. but no poi1lts of period grea'ter than tw or f hasnlore tllan one fixed point but no points of other periods. fL1rthermore.2. then f has more than one fixed point.has more one fixed point, ft1rthermore. and then f ha's a single fixed point. a singleperiod two orbit lying in but no points of period greater thantwo. where such that...