APD profiles and transfinite asymptotic dimension

被引：3
作者：
Orzechowski, Kamil [1 ]
机构：
[1] Univ Rzeszow, Inst Math, 1 Prof S Pigon St, PL-35310 Rzeszow, Poland
来源：
TOPOLOGY AND ITS APPLICATIONS | 2020年 / 283卷
关键词：
Asymptotic dimension; Asymptotic property C; Asymptotic property D; APD profile;
D O I：
10.1016/j.topol.2020.107394
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We develop the theory of APD profiles introduced by J. Dydak for infinity-pseudometric spaces ([3]). We connect them with transfinite asymptotic dimension defined by T. Radul ([4]). We give a characterization of spaces with transfinite asymptotic dimension at most omega + n for n is an element of omega and a sufficient condition for a space to have transfinite asymptotic dimension at most m center dot<bold> </bold>omega + n for m, n is an element of omega, using the language of APD profiles. This condition together with a result from [7] enables us to answer positively the question in [3, 5.15]. (C) 2020 Elsevier B.V. All rights reserved.
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页数：6
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