中文摘要：

本文研究了Cantor集和其并的自相似性.利用Cantor展式的方法,得到了关于Cantor集和迭代函数系的一个基本关系：T∪（T＋α）为自相似的当且仅当存在一个非负整数n使得α=±（k2-k1）dn.进一步,若T∪（T＋α）是自相似的,则它满足开集条件.

英文摘要：

In this article,the authors study the self-similarity of the union of Cantor sets.By the Cantor expressions they get a basic relationship between Cantor sets and iterated function systems：T ∪ （T＋ α） is a self-similar set iff there exists a natural number n ≥ 0,such that α=±（k2-k1）d n.Moreover,if T ∪ （T＋ α） is a self-similar set,it satisfies the open set condition.