Finitary approximations of coarse structures

A coarse structure $ \mathcal{E}$ on a set $X$ is called finitary if, for each entourage $E\in \mathcal{E}$, there exists natural number $n$ such that E[x]< n $x\in X$. By approximation of \mathcal{E}^\prime$, we mean any \mathcal{E}\subseteq \mathcal{E}^\prime$.If $\mathcal{E}^\prime$ has countable base and $E[x]$ finite X$ then \mathcal{E}^\prime$has cellular the relations linkness subsets $( X,\mathcal{E}^\prime)$ X, \mathcal{E})$ coincide.This answers Question 6 from [8]: class spaces not stable under linkness. We define apply strongest structure.