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- W3120314058 abstract "Let E be a metric space. We introduce a notion of connectedness index of E, which is the Hausdorff dimension of the union of non-trivial connected components of E. We show that the connectedness index of a fractal cube E is strictly less than the Hausdorff dimension of E provided that E possesses a trivial connected component. Hence the connectedness index is a new Lipschitz invariant. Moreover, we investigate the relation between the connectedness index and topological Hausdorff dimension." @default.
- W3120314058 created "2021-01-18" @default.
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- W3120314058 date "2021-05-01" @default.
- W3120314058 modified "2023-10-17" @default.
- W3120314058 title "A dimension drop phenomenon of fractal cubes" @default.
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- W3120314058 doi "https://doi.org/10.1016/j.jmaa.2020.124918" @default.
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