Proper absolute extensors

We describe the proper absolute (neighborhood) extensors for the class of at most $n$-dimensional spaces, notation ${\mathrm{A}(\mathrm{N})\mathrm{E}}_p(n)$. For example, the unique locally compact $n$-dimensional separable metric space $X\in {\mathrm{A}\mathrm{E}}_p(n)$ satisfiyng the $\mathrm{D}{\mathrm{D}}^{\mathrm{n}}\mathrm{P}$-property is the $n$-dimensional Menger compactum without a point. Non-metrizable ${\mathrm{A}(\mathrm{N})\mathrm{E}}_p(n)$-spaces are also described.