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Izv. Akad. Nauk SSSR Ser. Mat., 1986, Volume 50, Issue 1, Pages 156–180 (Mi izv1475)  

This article is cited in 14 scientific papers (total in 14 papers)

Noncompact absolute extensors in dimension $n$, $n$-soft mappings, and their applications

A. Ch. Chigogidze


Abstract: $R$-compact absolute extensors in dimension $n$ ($AE(n)$) and $n$-soft mappings are defined and studied. Spectral characterizations are obtained not only for $AE(n)$-spaces but also for $n$-soft mappings themselves; this is new even in the compact case. The technique developed is applied to the study of certain questions of functional analysis and the theory of nonmetrizable manifolds modeled on topological vector spaces.
Bibliography: 27 titles.

Full text: PDF file (4277 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1987, 28:1, 151–174

Bibliographic databases:

UDC: 513.83
MSC: Primary 54C10, 54C45, 54C55, 54F45; Secondary 54C15, 54A25, 54B25
Received: 24.02.1984

Citation: A. Ch. Chigogidze, “Noncompact absolute extensors in dimension $n$, $n$-soft mappings, and their applications”, Izv. Akad. Nauk SSSR Ser. Mat., 50:1 (1986), 156–180; Math. USSR-Izv., 28:1 (1987), 151–174

Citation in format AMSBIB
\Bibitem{Chi86}
\by A.~Ch.~Chigogidze
\paper Noncompact absolute extensors in dimension~$n$, $n$-soft mappings, and their applications
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1986
\vol 50
\issue 1
\pages 156--180
\mathnet{http://mi.mathnet.ru/izv1475}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=835570}
\zmath{https://zbmath.org/?q=an:0617.54015|0603.54018}
\transl
\jour Math. USSR-Izv.
\yr 1987
\vol 28
\issue 1
\pages 151--174
\crossref{https://doi.org/10.1070/IM1987v028n01ABEH000871}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. V. Fedorchuk, “Soft maps, multi-valued retractions, and functors”, Russian Math. Surveys, 41:6 (1986), 149–197  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. A. Ch. Chigogidze, “Compacta lying in the $n$-dimensional universal Menger compactum and having homeomorphic complements in it”, Math. USSR-Sb., 61:2 (1988), 471–484  mathnet  crossref  mathscinet  zmath
    3. A. Ch. Chigogidze, “$n$-shapes and $n$-cohomotopy groups of compacta”, Math. USSR-Sb., 66:2 (1990), 329–342  mathnet  crossref  mathscinet  zmath  isi
    4. A. Ch. Chigogidze, “The theory of $n$-shapes”, Russian Math. Surveys, 44:5 (1989), 145–174  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. V. V. Fedorchuk, “Probability measures in topology”, Russian Math. Surveys, 46:1 (1991), 45–93  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. M. M. Zarichnyi, “Absolute extensors and the geometry of multiplication of monads in the category of compacta”, Math. USSR-Sb., 74:1 (1993), 9–27  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. Murray Bell, Alex Chigogidze, “Topological groups homeomorphic to products of discrete spaces”, Topology and its Applications, 53:1 (1993), 67  crossref
    8. Alex Chigogidze, John R. Martin, “Fixed point sets of Tychonov cubes”, Topology and its Applications, 64:3 (1995), 201  crossref
    9. Dmitri Shakhmatov, Vesko Valov, “A characterization of Dugundji spaces via set-valued maps”, Topology and its Applications, 74:1-3 (1996), 109  crossref
    10. A. Chigogidze, K. Kawamura, E.D. Tymchatyn, “Nöbeling spaces and pseudo-interiors of Menger compacta”, Topology and its Applications, 68:1 (1996), 33  crossref
    11. Alex Chigogidze, John R. Martin, “Fixed point sets of autohomeomorphisms of uncountable products”, Topology and its Applications, 80:1-2 (1997), 63  crossref
    12. Alex Chigogidze, “Cohomological dimension of Tychonov spaces”, Topology and its Applications, 79:3 (1997), 197  crossref
    13. Vesko Valov, “Linear operators with compact supports, probability measures and Milyutin maps”, Journal of Mathematical Analysis and Applications, 370:1 (2010), 132  crossref
    14. Robert Alkins, Vesko Valov, “Functional extenders and set-valued retractions”, Journal of Mathematical Analysis and Applications, 2012  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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