一个一致连续性命题的错解剖析、反证及应用

Error Analysis,Counterexamples,and Applications Related to a Proposition about the Uniform Continuity of Functions

本文讨论关于函数一致连续性的一个重要命题,首先剖析常见的错误证明的原因,然后用反证法证明该命题并得到一个推论,最后举例说明其应用.

This paper addresses a key proposition about uniformly continuous functions.It begins by analyzing the reasons for common incorrect proofs,then proves the proposition by contradiction,derives several corollaries,and concludes with application examples.