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- W2358654324 abstract "This paper proposes a different method of proving Hausdorff dimension of Cantor set by considering character string or metric space. Using the principle of set finite covering and Lipschitz mapping, a mapping is constructed from the metric space that is defined by character string to Cantor set. The recurrence relationships are analyzed for the above mapping, which is shown to satisfy the biaxial Lipschitz inequality. It is proved that Hausdorff dimension of the metric space and that of Cantor set are equivalent. A method is found to prove Hausdorff dimension of Cantor set, which is different from the mass distribution principle, provides a way to avoid considering a suitable mass distribution, which is difficult, especially for the lower bound of the Hausdorff dimension, on its fractal set when applying the mass distribution principle for other complicated fractal sets, also has laid a theoretical foundation for studying the theories and methods for proving Hausdorff dimension, and the relations between character string and dimension." @default.
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- W2358654324 date "2009-01-01" @default.
- W2358654324 modified "2023-09-28" @default.
- W2358654324 title "A Proof of Hausdorff Dimension of Cantor Set" @default.
- W2358654324 hasPublicationYear "2009" @default.
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