  The Hausdorff-Alexandroff Theorem states that any compact metric space is the
continuous image of Cantor's ternary set $C$. It is well known that there are
compact Hausdorff spaces of cardinality equal to that of $C$ that are not
continuous images of Cantor's ternary set. On the other hand, every compact
countably infinite Hausdorff space is a continuous image of $C$. Here we
present a compact countably infinite non-Hausdorff space which is not the
continuous image of Cantor's ternary set.
