一类分形方块的拓扑豪斯道夫维数

Abstract

Abstract:

Balka, Buczolich, Elekes introduced a new concept of dimension for metric space, the so called topological Hausdorff dimension in[1]. The value of the topological Hausdorff dimension is always between the topological dimension and Husdorff dimension. Let n ≥ 2, D=d₁,d₂,…d_m⊆0,1,…,n-1² be a digit set. The set F satisfying the set equation F=1/n(F+D) is called a fractal square. In this paper, we mainly discuss the Topological Hausdorff Dimension of F in the case n=3, m ≤ 5.

Key words: Fractal square, Topological basis, Topological Hausdorff Dimension

CLC Number:

O211

Dai Yuxia, Ke Feng, Li Qing. The Topological Hausdorff Dimension of a Class of Fractal Squares[J].Acta mathematica scientia,Series A, 2017, 37(3): 519-527.

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The Topological Hausdorff Dimension of a Class of Fractal Squares

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