Abstract:
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.
Fulltext:
PDF file (954 kB)
