Geodesic
Axiomatic method of partitions in the theory
Sbornik. Mathematics, Tome 198 (2007) no. 3, pp. 299-342

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The Nöbeling space $N_k^{2k+1}$, a $k$-dimensional analogue of the Hilbert space, is considered; this is a topologically complete separable (that is, Polish) $k$-dimensional absolute extensor in dimension $k$ (that is, $\mathrm{AE}(k)$) and a strongly $k$-universal space. The conjecture that the above-listed properties characterize the Nöbeling space $N_k^{2k+1}$ in an arbitrary finite dimension $k$ is proved. In the first part of the paper a full axiom system of the Nöbeling spaces is presented and the problem of the improvement of a partition connectivity is solved on its basis. Bibliography: 29 titles. 
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     author = {S. M. Ageev},
     title = {Axiomatic method of partitions in the theory},
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S. M. Ageev. Axiomatic method of partitions in the theory. Sbornik. Mathematics, Tome 198 (2007) no. 3, pp. 299-342. http://geodesic.mathdoc.fr/item/SM_2007_198_3_a0/