Geodesic
Some dimensional results for a class of special homogeneous Moran sets
Czechoslovak Mathematical Journal, Tome 66 (2016) no. 1, pp. 127-135
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We construct a class of special homogeneous Moran sets, called $\{m_{k}\}$-quasi homogeneous Cantor sets, and discuss their Hausdorff dimensions. By adjusting the value of $\{m_{k}\}_{k\ge 1}$, we constructively prove the intermediate value theorem for the homogeneous Moran set. Moreover, we obtain a sufficient condition for the Hausdorff dimension of homogeneous Moran sets to assume the minimum value, which expands earlier works.
We construct a class of special homogeneous Moran sets, called $\{m_{k}\}$-quasi homogeneous Cantor sets, and discuss their Hausdorff dimensions. By adjusting the value of $\{m_{k}\}_{k\ge 1}$, we constructively prove the intermediate value theorem for the homogeneous Moran set. Moreover, we obtain a sufficient condition for the Hausdorff dimension of homogeneous Moran sets to assume the minimum value, which expands earlier works.
DOI : 10.1007/s10587-016-0245-2
Classification : 28A80
Keywords: homogeneous Moran set; $\{m_{k}\}$-Moran set; $\{m_{k}\}$-quasi homogeneous Cantor set; Hausdorff dimension 
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Hu, Xiaomei. Some dimensional results for a class of special homogeneous Moran sets. Czechoslovak Mathematical Journal, Tome 66 (2016) no. 1, pp. 127-135. doi: 10.1007/s10587-016-0245-2

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