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On strong embeddability and finite decomposition complexity

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Abstract

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.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, P. R. China

    Jun Xia & Xian Jin Wang

Authors
  1. Jun Xia
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  2. Xian Jin Wang
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Correspondence to Jun Xia.

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Supported by National Natural Science Foundation of China (Grant No. 11231002)

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Xia, J., Wang, X.J. On strong embeddability and finite decomposition complexity. Acta. Math. Sin.-English Ser. 33, 403–418 (2017). https://doi.org/10.1007/s10114-016-5761-3

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  • DOI: https://doi.org/10.1007/s10114-016-5761-3

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