Approximation by poised sets of nodes

In the present paper it has been shown that nodes of any finite set $X\subset\mathbb{R}^d$ can be made independent by arbitrarily small perturbation, in other words, the set $X$ can be approximated by sets of independent nodes. In the case of $\#X=\mathrm{dim}\prod^d_n$ the set $X$ can be approximated by sets of poised nodes.