Some dimensional results for a class of special homogeneous Moran sets

Czechoslovak Mathematical Journal

Xiaomei Hu¹ 

[1] School of Mathematics and Statistics, Central China Normal University, No. 152 Luoyu Road, Hongshan Zone, Wuhan, 430079, Hubei, P. R. China

关键词: homogeneous Moran set;    $\{m_k\}$-Moran set;    $\{m_k\}$-quasi homogeneous Cantor set;    Hausdorff dimension;   

DOI  :  

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

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 $\{m_k\}_{k\ge1}$, 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.

【 授权许可】

Unknown