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

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.