Abstract
We construct a class of special homogeneous Moran sets, called {mk}-quasi homogeneous Cantor sets, and discuss their Hausdorff dimensions. By adjusting the value of {mk}k⩽1, 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.
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