我们知道 ,在人类将数的概念由正整数集合扩充到复数集的过程中 ,主要是为了解决代数运算的封闭问题 .本文就函数的封闭性作初步探讨 .1　封闭函数的定义定义 :设函数ｙ=ｆ(ｘ) ,ｘ∈Ａ ,如果对于任意ｘ ∈Ａ ,都有ｆ(ｋ) (ｘ) =ｘ(其中ｆ(ｋ) (ｘ) =ｆ( ｆ(…ｆｋ个ｆ(ｘ) ) ) We know that in the process of human expansion of the concept of numbers from a positive integer set to a complex set, it is mainly to solve the problem of the closure of algebraic operations. This paper makes a preliminary discussion on the closedness of functions. 1 Definition of closed function Definition: Set function y=f(x) ,x∈A, if for any x ∈A , there is f(k) (x) =x (where f(k) (x) =f( f(...fkf(x) ))