Some dimensional results for a class of special homogeneous Moran sets

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) } (ka (c) 1/21), we constructively prove the intermediate value theorem for the homogeneous Moran set. Moreover, we obtain a sufficient condition for the Hausdorff dimension of ho- mogeneous Moran sets to assume the minimum value, which expands earlier works.