Nonarchimedean Cantor set and string

We construct a nonarchimedean (or p-adic) analogue of the classical ternary Cantor set . In particular, we show that this nonarchimedean Cantor set is self-similar. Furthermore, we characterize as the subset of 3-adic integers whose elements contain only 0’s and 2’s in their 3-adic expansions and prove that is naturally homeomorphic to . Finally, from the point of view of the theory of fractal strings and their complex fractal dimensions 7, 8], the corresponding nonarchimedean Cantor string resembles the standard archimedean (or real) Cantor string perfectly. Dedicated to Vladimir Arnold, on the occasion of his jubilee