In this paper, we study the w-limit sets of the interval containing an infinite minimal set. We show that for a non-chaotic function f, the intersection of two different w-limit sets is either empty or contains an infinite minimal set. As an application of the main result, we also give alternative proofs for some well known results related to the structure of w-limit sets of a non-chaotic function f.

periodic points, recurrent points, nonwandering points, w-limit set, minimal set, non-chaotic map.