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

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.

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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

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
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
3. A. Ch. Chigogidze, “$n$-shapes and $n$-cohomotopy groups of compacta”, Math. USSR-Sb., 66:2 (1990), 329–342
4. A. Ch. Chigogidze, “The theory of $n$-shapes”, Russian Math. Surveys, 44:5 (1989), 145–174
5. V. V. Fedorchuk, “Probability measures in topology”, Russian Math. Surveys, 46:1 (1991), 45–93
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
7. Murray Bell, Alex Chigogidze, “Topological groups homeomorphic to products of discrete spaces”, Topology and its Applications, 53:1 (1993), 67
8. Alex Chigogidze, John R. Martin, “Fixed point sets of Tychonov cubes”, Topology and its Applications, 64:3 (1995), 201
9. Dmitri Shakhmatov, Vesko Valov, “A characterization of Dugundji spaces via set-valued maps”, Topology and its Applications, 74:1-3 (1996), 109
10. A. Chigogidze, K. Kawamura, E.D. Tymchatyn, “Nöbeling spaces and pseudo-interiors of Menger compacta”, Topology and its Applications, 68:1 (1996), 33
11. Alex Chigogidze, John R. Martin, “Fixed point sets of autohomeomorphisms of uncountable products”, Topology and its Applications, 80:1-2 (1997), 63
12. Alex Chigogidze, “Cohomological dimension of Tychonov spaces”, Topology and its Applications, 79:3 (1997), 197
13. Vesko Valov, “Linear operators with compact supports, probability measures and Milyutin maps”, Journal of Mathematical Analysis and Applications, 370:1 (2010), 132
14. Robert Alkins, Vesko Valov, “Functional extenders and set-valued retractions”, Journal of Mathematical Analysis and Applications, 2012
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