In 1984, Kurt Mahler posed the following fundamental question: How well can
irrationals in the Cantor set be approximated by rationals in the Cantor set?
Towards development of such a theory, we prove a Dirichlet-type theorem for
this intrinsic diophantine approximation on Cantor-like sets, and discuss
related possible theorems/conjectures. The resulting approximation function is
analogous to that for R^d, but with d being the Hausdorff dimension of the set,
and logarithmic dependence on the denominator instead.Comment: 7 pages, 0 figure