Abstract
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⩽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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The research has been supported by the National Natural Science Foundation of China No. 11271148.
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Hu, X. Some dimensional results for a class of special homogeneous Moran sets. Czech Math J 66, 127–135 (2016). https://doi.org/10.1007/s10587-016-0245-2
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DOI: https://doi.org/10.1007/s10587-016-0245-2