QUASI-LOWER DIMENSION AND QUASI-LIPSCHITZ MAPPING

被引：13
|
作者：
Chen, Haipeng [1 ]
Du, Yali [2 ]
Wei, Chun [3 ]
机构：
[1] South China Univ Technol, Dept Math, Guangzhou 510641, Guangdong, Peoples R China
[2] Univ Sao Paulo, Inst Math & Stat, BR-05508090 Sao Paulo, SP, Brazil
[3] Zhongnan Univ Econ & Law, Sch Math & Stat, Wuhan 430073, Peoples R China
来源：
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY | 2017年 / 25卷 / 03期
关键词：
Quasi-Lower Dimension; Quasi-Lipschitz Mapping; Sets Defined by Digit Restrictions; CANTOR SETS; MORAN SETS; EQUIVALENCE; FRACTALS;
D O I：
10.1142/S0218348X17500347
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we show that the lower dimension is not invariant under quasi-Lipschitz mapping, and then we find an invariant named the quasi-lower dimension. We also compute the quasi-lower dimension of a class of sets defined by digit restrictions, and then give an example to distinguish the quasi-lower dimension and other dimensions.
引用
收藏
页数：9
相关论文
共 50 条
  • [31] Lipschitz structure of quasi-Banach spaces
    Albiac, F.
    Kalton, N. J.
    ISRAEL JOURNAL OF MATHEMATICS, 2009, 170 (01) : 317 - 335
  • [32] QUASI-SYMMETRIC AND LIPSCHITZ APPROXIMATION OF EMBEDDINGS
    LUUKKAINEN, J
    TUKIA, P
    ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 1981, 6 (02): : 343 - 367
  • [33] LIPSCHITZ AND QUASI-CONFORMAL APPROXIMATION AND EXTENSION
    TUKIA, P
    VAISALA, J
    ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 1981, 6 (02): : 303 - 342
  • [34] STUDY OF QUASI-LOWER AND UPPER BOUNDS OF COLLAPSE LOAD OF SHELLS OF REVOLUTION BY FINITE-ELEMENT METHOD AND NON-LINEAR PROGRAMMING
    HUNG, ND
    TRAPLETTI, M
    RANSART, D
    INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, 1978, 13 (02) : 79 - 102
  • [35] Visual Clustering Method of Quasi-Circular Mapping Based on Dimension Extension and Rearrangement
    Huang S.
    Li M.
    Chen H.
    Li J.
    Zhang C.
    Moshi Shibie yu Rengong Zhineng/Pattern Recognition and Artificial Intelligence, 2019, 32 (04): : 326 - 335
  • [36] Quasi-Assouad dimension of fractals
    Lu, Fan
    Xi, Li-Feng
    JOURNAL OF FRACTAL GEOMETRY, 2016, 3 (02) : 187 - 215
  • [37] PROPERTIES OF QUASI-ASSOUAD DIMENSION
    Garcia, Ignacio
    Hare, Kathryn
    ANNALES FENNICI MATHEMATICI, 2021, 46 (01): : 279 - 293
  • [38] Difference dimension quasi-polynomials
    Levin, Alexander
    ADVANCES IN APPLIED MATHEMATICS, 2017, 89 : 1 - 17
  • [39] QUASI-MEASURES AND DIMENSION THEORY
    WHEELER, RF
    TOPOLOGY AND ITS APPLICATIONS, 1995, 66 (01) : 75 - 92
  • [40] A lower bound on the size of Lipschitz subsets in dimension 3
    Matousek, J
    COMBINATORICS PROBABILITY & COMPUTING, 2003, 12 (04): : 427 - 430
12345