[1]饶 峰,柯 枫.拓扑Hausdorff维数的一种计算方法及其应用[J].四川师范大学学报(自然科学版),2017,(04):496-502.[doi:10.3969/j.issn.1001-8395.2017.04.012 ]
 RAO Feng,KE Feng.A Calculation Method of the Topological Hausdorff Dimension and Its Applications[J].Journal of SichuanNormal University,2017,(04):496-502.[doi:10.3969/j.issn.1001-8395.2017.04.012 ]
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拓扑Hausdorff维数的一种计算方法及其应用()
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《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
期数:
2017年04期
页码:
496-502
栏目:
基础理论
出版日期:
2017-04-30

文章信息/Info

Title:
A Calculation Method of the Topological Hausdorff Dimension and Its Applications
文章编号:
1001-8395(2017)04-0496-07
作者:
饶 峰12 柯 枫2
1.湖北商贸学院 基础课部, 湖北 武汉 430079;
2.湖北大学 数学与统计学院, 湖北 武汉 430062
Author(s):
RAO Feng12 KE Feng2
1. Fundamental Course Department, Hubei Business College, Wuhan 430079, Hubei;
2. School of Mathematics and Statistics, Hubei University, Wuhan 430062, Hubei
关键词:
Hausdorff维数 拓扑维数 拓扑Hausdorff维数 分形方块
Keywords:
Hausdorff dimension topological dimension topological Hausdorff dimension fractal square
分类号:
O189
DOI:
10.3969/j.issn.1001-8395.2017.04.012
文献标志码:
A
摘要:
介绍平面上集合的拓扑Hausdorff维数的一种计算方法,此方法是根据集合的几何特征构造它的一个基,利用基的边界的Hausdorff维数获得该集合的拓扑Hausdorff维数.利用此方法计算了一类分形方块的拓扑Hausdorff维数.
Abstract:
A calculation method of the topological Hausdorff dimension of a set on a plane is introduced. This method is to construct a basis of the set and then use Hausdorff dimension of the boundary of the basis to obtain the topological Hausdorff dimension of this set. We calculate the topological Hausdorff dimensions of a class of fractal squares by this method.

参考文献/References:

[1] FALCONER K J. Fractal Geometry:Mathematical Foundations and Applications[M]. 2nd. England:John Wiley,2003:31-119.
[2] HUREWICZ W, WALLMAN H. Dimension Theory[M]. Princeton:Princeton Uiversity Press,1948:12-20.
[3] BALKA R, BUCZOLICH Z, ELEKES M. A new fractal dimension:the topological Hausdorff dimension[J]. Adv Math,2015,274(1):881-927.
[4] 熊金城. 点集拓扑讲义[M]. 北京:高等教育出版社,2011:82-83.
[5] BALKA R. Inductive topological Hausdorff dimensions and fibers of generic continuous functions[J]. Monatsh Math,2014,174(1):1-28.
[6] BALKA R, BUCZOLICH Z, ELEKES M. Topological Hausdorff dimension and level sets of generic continuous functions on fractals[J]. Chaos Solitons Fractals,2012,45(12):1579-1589.
[7] BALKA R, FARKAS A, FRASER J M, et al. Dimension and measure for generic continuous images[J]. Ann Acad Sci Fenn Math,2013,38:389-404.
[8] MAULDIN R D, WILLIAMS S C. On the Hausdorff dimension of some graphs[J]. Trans Am Math Soc,1986,298(2):793-803.
[9] HYDE J T, LASCHOS V, OLSEN L, et al. On the box dimensions of graphs of typical continuous functions[J]. J Math Anal Appl,2012,391(2):567-581.
[10] FALCONER K J. On the Hausdorff dimension of distance sets[J]. Mathematika,1985,32(2):206-212.
[11] WHYBURN G T. Topological characterization of the Sierpiński curve[J]. Fund Math,1958,45(6):1090-1099.

备注/Memo

备注/Memo:
收稿日期:2016-08-24
基金项目:湖北省教育厅科学技术研究项目(B2016480)
第一作者简介:饶 峰(1977—),男,讲师,主要从事分形几何的研究,E-mail:601682168@qq.com
更新日期/Last Update: 2017-04-30