Classification of metric spaces with infinite asymptotic dimension

被引：8
作者：
Wu, Yan [1 ]
Zhu, Jingming [1 ]
机构：
[1] Jiaxing Univ, Coll Math Phys & Informat Engn, Jiaxing 314001, Peoples R China
来源：
TOPOLOGY AND ITS APPLICATIONS | 2018年 / 238卷
关键词：
Asymptotic dimension; Transfinite asymptotic dimension; Asymptotic property C; PROPERTY C;
D O I：
10.1016/j.topol.2018.02.001
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We introduce a geometric property called complementary-finite asymptotic dimension (coasdim). Similar to the case of asymptotic dimension, we prove the corresponding coarse invariant theorem, union theorem and Hurewicz-type theorem. Moreover, we show that coasdim(X) <= omega + k implies trasdim(X) <= omega + k and transfinite asymptotic dimension of the shift union sh boolean OR circle plus(infinity)(i=1) 2(i)Z is no more than omega + 1, i.e. trasdim(sh boolean OR circle plus(infinity)(i=1) 2(i)Z) <= omega + 1. (C) 2018 Elsevier B.V. All rights reserved.
引用
收藏
页码：90 / 101
页数：12
相关论文
共 9 条
[1]  
Bell G., 2011, Topology Proc., V38, P209
[2]   A Hurewicz-type theorem for asymptotic dimension and applications to geometric group theory [J].
Bell, G. C. ;
Dranishnikov, A. N. .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2006, 358 (11) :4749-4764
[3]   Asymptotic dimension, decomposition complexity, and Haver's property C [J].
Dranishnikov, Alexander ;
Zarichnyi, Michael .
TOPOLOGY AND ITS APPLICATIONS, 2014, 169 :99-107
[4]   Asymptotic topology [J].
Dranishnikov, AN .
RUSSIAN MATHEMATICAL SURVEYS, 2000, 55 (06) :1085-1129
[5]  
Engelking R., 1995, Theory of dimensions: finite and infinite
[6]  
Gromov M., 1993, Geometric group theory, Vol. 2 (Sussex, V182, P1
[7]   On transfinite extension of asymptotic dimension [J].
Radul, T. .
TOPOLOGY AND ITS APPLICATIONS, 2010, 157 (14) :2292-2296
[8]  
Satkiewicz M., 2012, ARXIV13101258 MATH G
[9]   Asymptotic property C of the countable direct sum of the integers [J].
Yamauchi, Takamitsu .
TOPOLOGY AND ITS APPLICATIONS, 2015, 184 :50-53
1