RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Sb., 2007, Volume 198, Number 3, Pages 3–50 (Mi msb1476)  

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: PDF file (954 kB)
References: PDF file   HTML file

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
\Bibitem{Age07}
\by S.~M.~Ageev
\paper Axiomatic method of partitions in the theory
of N\"obeling spaces.
I.~Improvement of partition connectivity
\jour Mat. Sb.
\yr 2007
\vol 198
\issue 3
\pages 3--50
\mathnet{http://mi.mathnet.ru/msb1476}
\crossref{https://doi.org/10.4213/sm1476}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2354278}
\zmath{https://zbmath.org/?q=an:1147.54019}
\elib{http://elibrary.ru/item.asp?id=9469179}
\transl
\jour Sb. Math.
\yr 2007
\vol 198
\issue 3
\pages 299--342
\crossref{https://doi.org/10.1070/SM2007v198n03ABEH003838}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000247946700001}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34547851566}


Linking options:
  • http://mi.mathnet.ru/eng/msb1476
  • https://doi.org/10.4213/sm1476
  • http://mi.mathnet.ru/eng/msb/v198/i3/p3

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
    Cycle of papers

    This publication is cited in the following articles:
    1. S. M. Ageev, “Axiomatic method of partitions in the theory of Nöbeling spaces. II. Unknotting theorem”, Sb. Math., 198:5 (2007), 597–625  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. 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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. Levin M., “A $Z$-set unknotting theorem for Nöbeling spaces”, Fund. Math., 202:1 (2009), 1–41  crossref  mathscinet  zmath  isi  scopus
    4. Ageev S.M., Cencelj M., Repovš D., “Preserving $Z$-sets by Dranishnikov's resolution”, Topology Appl., 156:13 (2009), 2175–2188  crossref  mathscinet  zmath  isi  scopus
    5. Dranishnikov A.N., “Characterization and Topological Rigidity of Nobeling Manifolds”, Mem. Am. Math. Soc., 223:1048 (2013), 3+  mathscinet  isi
    6. Pol E., Pol R., “Note on Isometric Universality and Dimension”, Isr. J. Math., 209:1 (2015), 187–197  crossref  mathscinet  zmath  isi  elib  scopus
    7. 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  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
    Number of views:
    This page:327
    Full text:103
    References:27
    First page:5

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019