Nonarchimedean Cantor set and string
نویسنده
چکیده
We construct a nonarchimedean (or p-adic) analogue of the classical ternary Cantor set C. In particular, we show that this nonarchimedean Cantor set C3 is self-similar. Furthermore, we characterize C3 as the subset of 3-adic integers whose elements contain only 0’s and 2’s in their 3-adic expansions and prove that C3 is naturally homeomorphic to C. 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. Mathematics Subject Classification (2000). Primary 11M41, 26E30, 28E30, 28A12, 26A80; Secondary 11M36, 12J25, 28A75, 28A78.
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