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Keywords:
homogeneous Moran set; $\{m_{k}\}$-Moran set; $\{m_{k}\}$-quasi homogeneous Cantor set; Hausdorff dimension
homogeneous Moran set; $\{m_{k}\}$-Moran set; $\{m_{k}\}$-quasi homogeneous Cantor set; Hausdorff dimension
Summary:
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.
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