AbstractsMathematics

The Cantor set is a compact, totally disconnected, perfect subset of the real line. In this paper it is shown that two non-empty, compact, totally disconnected, perfect metric spaces are homeomorphic. Furthermore, a subset of the real line is homeomorphic to the Cantor set if and only if it is obtained from a closed interval by removing a class of disjoint, separated from each other but sufficiently dense open intervals.