Products of Cantor's discontinuum (Q1088187)

Let K be the Cantor set. The author observes that \(K^ n\) and \(K^{\aleph_ 0}\) can be shown to be homeomorphic to K by actually constructing the appropriate homeomorphism. The mapping \(f:K^ n\to K\) that works is an ''interlacing'' of the unique decimal expansion for the coordinates of points in \(K^ n\). A diagonalization of this idea is used to obtain the corresponding map for \(f: K^{\aleph_ 0}\to K\).