A metric space $(X,d)$ has the de Groot property $GP_n$ if for any points
$x_0,x_1,...,x_{n+2}\in X$ there are positive indices $i,j,k\le n+2$ such that
$i\ne j$ and $d(x_i,x_j)\le d(x_0,x_k)$. If, in addition, $k\in\{i,j\}$ then
$X$ is said to have the Nagata property $NP_n$. It is known that a compact
metrizable space $X$ has dimension $dim(X)\le n$ iff $X$ has an admissible
$GP_n$-metric iff $X$ has an admissible $NP_n$-metric.