On strong embeddability and finite decomposition complexity
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- 作者：Jun Xia ; Xian Jin Wang
- 关键词：Metric geometry ; strong embeddability ; coarse invariance ; permanence properties ; finite
- 刊名：Acta Mathematica Sinica, English Series
- 出版年：2017
- 出版时间：March 2017
- 年：2017
- 卷：33
- 期：3
- 页码：403-418
- 全文大小：
- 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics, general;
- 出版者：Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
- ISSN：1439-7617
- 卷排序：33
文摘
The strong embeddability is a notion of metric geometry, which is an intermediate property lying between coarse embeddability and property A. In this paper, we study the permanence properties of strong embeddability for metric spaces. We show that strong embeddability is coarsely invariant and it is closed under taking subspaces, direct products, direct limits and finite unions. Furthermore, we show that a metric space is strongly embeddable if and only if it has weak finite decomposition complexity with respect to strong embeddability.