一个不是任何连续函数列的极限的函数

On Function That Is Not The Limit of Any Sequence of Continuous Functions

本文借助于度量空间证明了:在R′上不存在收敛于无理数集的特征函数X(x)的连续函数序列{f_m(x)}.

In this papaer, the following theorem is proved by means of the resultsof metric spaces: There is no sequence {fn(x)} of continuous functions, such that(?) fn(x) = χ(x), (-∞<x<+∞)where x(x) is a characteristic function, i、e., (?)1, x is an irrational number, (?)0, x is a rational number.