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On coarse Lipschitz embeddability into $c_0(\kappa )$

Volume 241 / 2018

Andrew Swift Fundamenta Mathematicae 241 (2018), 67-81 MSC: Primary 46B20; Secondary 46T99. DOI: 10.4064/fm383-3-2017 Published online: 11 August 2017

Abstract

In 1994, Jan Pelant proved that a metric property related to the notion of paracompactness called the uniform Stone property characterizes a metric space’s uniform embeddability into $c_0(\kappa )$ for some cardinality $\kappa $. In this paper it is shown that coarse Lipschitz embeddability of a metric space into $c_0(\kappa )$ can be characterized in a similar manner. It is also shown that coarse, uniform, and bi-Lipschitz embeddability into $c_0(\kappa )$ are equivalent notions for normed linear spaces.

Authors

  • Andrew SwiftDepartment of Mathematics
    Texas A&M University
    College Station, TX 77843, U.S.A.
    e-mail

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