Relative Property A for Discrete Metric Space
Received:May 01, 2018  Revised:August 12, 2018
Key Word: relative Property A   coarse embedding   mazur map
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.11701301).
 Author Name Affiliation Yufang LI Department of Mathematics, Zhejiang University, Zhejiang 310058, P. R. China Department of Mathematics and Statistics, Guizhou University, Guizhou 550025, P. R. China Zhe DONG Department of Mathematics, Zhejiang University, Zhejiang 310058, P. R. China Yuanyi WANG School of Information Engineering, College of Science and Technology, Ningbo University, Zhejiang 315211, P. R. China
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Yu introduced Property A on discrete metric spaces. In this paper, a relative Property A for a discrete metric space $X$ with respect to a set $Y$ and a map $\rho_{X,Y}$ is defined. Some characterizations for relative Property A are given. In particular, a discrete metric space with relative Property A can be coarse embedding into a Hilbert space under certain condition.