保维逼近

摘要：

本文提出了定义在$[0,1]$上的连续函数的保维逼近的新概念，并对它进行了初步的研究，研究了连续函数关于分形维数的限制和扩张。

英文摘要：

This article introduces the novel notion of dimension preserving approximation for continuous functions defined on $[0,1]$ and initiates the study of it. Restrictions and extensions of continuous functions in regards to fractal dimensions are also investigated.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。