Continuous Images of Cantor's Ternary Set.

The article reports that the Hausdorff-Alexandroff Theorem states that any compact metric space is the continuous image of Cantor's ternary set C. Restricting the cardinality leads to a sufficient condition. the cardinality of a space, which is the continuous image of C. The restriction on cardinality is a necessary and there are compact Hausdorff spaces with cardinality.