Topological Hausdorff dimension of fractal squares and its application to Lipschitz classification

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. (paper)