Cantor集与Cantor函数性质探究

Research on the Properties of Cantor Sets and Cantor Functions

摘要: Cantor集是由德国数学家格奥尔格·康托尔在1883年引入的。因其构思精巧且性质独特，Cantor集应用广泛并且为众多数学问题提供了解决的思路和方法。而Cantor函数是由Cantor集构造的，它的特异性质也可以应用在很多数学问题中。它们特殊奇妙的性质使得其获得无与伦比的魅力，吸引了众多数学工作者对它进行探索和研究。本文从Cantor集与Cantor函数的构造出发，重点探讨了Cantor集与Cantor函数的性质。

Abstract: The Cantor set was introduced by the German mathematician Georg Cantor in 1883. Because of its ingenious conception and unique nature, Cantor set is widely used and provides ideas and methods for solving many mathematical problems. Cantor function is constructed from Cantor set, and its special properties can also be applied to many mathematical problems. Their special and wonderful nature makes them incomparable charm, which attracts many mathematicians to explore and study them. Starting from the construction of Cantor set and Cantor function, this paper mainly discusses the properties of Cantor set and Cantor function.