Cantor Sets

Abstract

The Cantor set is an interesting example of an uncountable set of measure zero and has many interesting properties and consequences in the fields of set theory, topology, and fractal theory. The principal aim of this paper is to introduce a generator of finite subsets of the basic Cantor (ternary) set and its generalization to the Cantor n-ary set. We compute the fractal dimension of these Cantor sets.