Chigogidze's unstable Nöbeling space universality conjecture

Let $N^n_m$ be the subset of $\mathbb{R}^n$ consisting of points with at most $m$ rational coordinates. Chigogidze's conjecture. Every $m$-dimensional subset of $\mathbb{R}^n$ can be embedded into $N^n_m$. This is the main part of the conjectured characterization of unstable Nöbeling spaces, where instability means $n<2m+1$. The conjecture is presented as open in the source, and is attributed there to Chigogidze (1996).