康托集与康托函数的推广

The Generalization of Cantor Sets and Cantor Functions

本文在康托三分集的基础上定义了康托五分集,康托七分集,康托2k+1(其中k是任意给定的自然数)分集,并给出了它们的一些性质,同时,在给定的范围内推广了康托函数的定义及性质。

In this paper, on the basis of Cantor ternaty sets, Cantor five dividingsets, Cantor seven dividing sets and Cantor 2k + 1 dividing sets (where k is an arbi-traty given natural number) are defined, and their some properties are given. Inthe meanwhile, the definitions and properties of Cantor functions are being gener-alized within the given range.