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 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.

引用

页数：6

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