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This article is cited in 7 scientific papers (total in 7 papers)
Axiomatic method of partitions in the theory
of Nöbeling spaces.
I. Improvement of partition connectivity
S. M. Ageev
Belarusian State University, Faculty of Mathematics and Mechanics
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.
DOI:
https://doi.org/10.4213/sm1476
 Full text:
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English version:
Sbornik: Mathematics, 2007, 198:3, 299–342
Bibliographic databases:
    
UDC:
515.124.62+515.125
MSC: Primary 55P15, 54F45, 54F65; Secondary 54C55
Received: 09.12.2005 and 29.11.2006
Citation:
S. M. Ageev, “Axiomatic method of partitions in the theory
of Nöbeling spaces.
I. Improvement of partition connectivity”, Mat. Sb., 198:3 (2007), 3–50; Sb. Math., 198:3 (2007), 299–342
Citation in format AMSBIB
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I.~Improvement of partition connectivity
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Linking options:
http://mi.mathnet.ru/eng/msb1476https://doi.org/10.4213/sm1476 http://mi.mathnet.ru/eng/msb/v198/i3/p3
Citing articles on Google Scholar:
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English citations
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Cycle of papers
This publication is cited in the following articles:
-
S. M. Ageev, “Axiomatic method of partitions in the theory of
Nöbeling spaces. II. Unknotting theorem”, Sb. Math., 198:5 (2007), 597–625
 -
S. M. Ageev, “Axiomatic method of partitions in the theory of Nöbeling spaces.
III. Consistency of the axiom system”, Sb. Math., 198:7 (2007), 909–934
-
Levin M., “A $Z$-set unknotting theorem for Nöbeling spaces”, Fund. Math., 202:1 (2009), 1–41
-
Ageev S.M., Cencelj M., Repovš D., “Preserving $Z$-sets by Dranishnikov's resolution”, Topology Appl., 156:13 (2009), 2175–2188
-
Dranishnikov A.N., “Characterization and Topological Rigidity of Nobeling Manifolds”, Mem. Am. Math. Soc., 223:1048 (2013), 3+
-
Pol E., Pol R., “Note on Isometric Universality and Dimension”, Isr. J. Math., 209:1 (2015), 187–197
-
Dijkstra J.J. Levin M. Van Mill J., “A short proof of Toruńczyk's characterization theorems”, Proc. Amer. Math. Soc., 145:2 (2017), 901–914
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