We calculate topological Hausdorff dimensions of a class of fractal squares by constructing certain self-similar curves. Examples include some generalized Sierpiński carpets, which have the same Hausdorff dimensions but different topological Hausdorff dimensions. Applications are given to the study of Lipschitz equivalence of fractal squares.

中文翻译：

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分形正方形的Hausdorff拓扑维数及其在Lipschitz分类中的应用

我们通过构造某些自相似曲线来计算一类分形正方形的Hausdorff拓扑尺寸。示例包括一些通用的Sierpiński地毯，它们具有相同的Hausdorff尺寸，但是拓扑上的Hausdorff尺寸不同。分形平方的Lipschitz等价研究得到了应用。