分形正方形拓扑豪斯多夫维数的估计值

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-06-28 DOI:10.1016/j.topol.2024.109003

Jian-Ci Xiao

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引用次数: 0

摘要

在本文中，我们首先获得了分形正方形拓扑豪斯多夫维数的一些上限。作为推论，我们给出了一类特殊分形正方形的该维度公式。结合之前的结果，我们还完成了三阶分形正方形拓扑豪斯多夫维度的计算。其中有些维度需要非难的基构造。我们的研究结果还揭示了分形正方形的 Lipschitz 分类。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Estimates on the topological Hausdorff dimensions of fractal squares

We first obtain some upper bounds on the topological Hausdorff dimensions of fractal squares. As a corollary, we give the formula for this dimension of a special class of fractal squares. Combined with previous results, we also complete the computation of the topological Hausdorff dimensions of fractal squares of order three. Some of these require non-trivial constructions of bases. Our results also shed light on the Lipschitz classification of fractal squares.

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来源期刊

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.