Abstract
Given two metric spaces E,F, it is well known that, dimHE +dimHF ≤ dimH(E × F) ≤dimHE +dimPF, dimHE +dimPF ≤ dimP(E × F) ≤dimPE +dimPF, where dimHE, dimPE denote, respectively, the Hausdorff and packing dimension of E. In this paper, we show that, for any 0 ≤ s,t ≤ 1, there exist E,F a" such that the following equalities hold simultaneously: dimH(E × F)-dimHE-dimHF = s, dimPE +dimPF-dimP(E × F) = t. This complete the related results of Wei et al. [C. Wei, S. Y. Wen and Z. X. Wen, Remarks on dimensions of Cartesian product sets, Fractals 24(3) (2016) 1650031].
Original language | English |
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Article number | 1750052 |
Journal | Fractals |
Volume | 25 |
Issue number | 6 |
DOIs | |
Publication status | Published - 1 Dec 2017 |
Keywords
- Cartesian Product
- Hausdorff Dimension
- Moran Sets
- Packing Dimension
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Jiang, X., Liu, Q., & Wen, Z. (2017). An intermediate value property of fractal dimensions of cartesian product. Fractals, 25(6), Article 1750052. https://doi.org/10.1142/S0218348X17500529