Abstract:
In this paper there is an investigation, for the case of a compact group G, of the orbit space X/G of a given G-space X, from the point of view of the theory of retracts. A particular case of the main result asserts that if one of the spaces X and G has countable weight and X is a G-A(N)R for metrizable spaces, then X/G is an A(N)R for metrizable spaces.
New results about the equivariant embedding of metrizable G-spaces are also obtained.
Bibliography: 28 titles.
\Bibitem{Ant88}
\by S.~A.~Antonyan
\paper Retraction properties of an orbit space
\jour Math. USSR-Sb.
\yr 1990
\vol 65
\issue 2
\pages 305--321
\mathnet{http://mi.mathnet.ru/eng/sm1788}
\crossref{https://doi.org/10.1070/SM1990v065n02ABEH001311}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=976513}
\zmath{https://zbmath.org/?q=an:0685.54013}
Linking options:
https://www.mathnet.ru/eng/sm1788
https://doi.org/10.1070/SM1990v065n02ABEH001311
https://www.mathnet.ru/eng/sm/v179/i3/p300
This publication is cited in the following 23 articles:
Jorge Alberto Sánchez Martínez, Yazmín Hernández Chávez, Gerardo Hernández Chávez, “A lighthearted proof of the existence of G-fibrant extensions”, Topology and its Applications, 347 (2024), 108884
Sergey A. Antonyan, “Equivariant Insight into Hyperspaces of convex bodies”, Topology and its Applications, 2024, 109096
West J., “Involutions of Hilbert Cubes That Are Hyperspaces of Peano Continua”, Topology Appl., 240 (2018), 238–248
Belegradek I., “Hyperspaces of Smooth Convex Bodies Up to Congruence”, Adv. Math., 332 (2018), 176–198
Antonyan S.A., Jonard-Perez N., Juarez-Ordonez S., “Hyperspaces of Keller Compacta and their Orbit Spaces”, J. Math. Anal. Appl., 412:2 (2014), 613–619
Alexander Bykov, Amalia Torres Juan, “Fibrant extensions of free G-spaces”, Topology and its Applications, 2011
Sibe Mardesic, “On inverse limits of compact spaces. Correction of a proof”, Glas. Mat. Ser. III, 45:2 (2010), 525
S. M. Ageev, D. Repovš, “On extending actions of groups”, Sb. Math., 201:2 (2010), 159–182
Antonyan S., “A Characterization of Equivariant Absolute Extensors and the Equivariant Dugundji Theorem”, Houst. J. Math., 31:2 (2005), 451–462
S. A. Antonyan, “New topological models for Banach–Mazur compacta”, J. Math. Sci., 146:1 (2007), 5465–5473
Sergey Antonyan, “West's problem on equivariant hyperspaces and Banach-Mazur compacta”, Trans. Amer. Math. Soc., 355:8 (2003), 3379
S. M. Ageev, D. Repovš, “The Jaworowski Method in the Problem of the Preservation of Extensor Properties by the Orbit Functor”, Math. Notes, 71:3 (2002), 428–431
Sergei M. Ageev, Duŝan Repovŝ, “On Banach-Mazur compacta”, J Austral Math Soc, 69:3 (2000), 316
S. A. Antonyan, “Based free compact Lie group actions on the Hilbert cube”, Math. Notes, 65:2 (1999), 135–143
Antonyan S., “Extensorial Properties of Orbit Spaces of Proper Group Actions”, Topology Appl., 98:1-3 (1999), 35–46
Ageev S., Bogatyi S., Fabel P., “The Banach-Mazur Compactum Q(N) Is an Ar”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1998, no. 1, 11–13
S. A. Antonyan, “Existence of a cut for arbitrary compact transformations groups”, Math. Notes, 56:5 (1994), 1101–1104
Antonian S., “Preservation of K-Connectedness and Local K-Connectedness by Symmetrical Degree Functor”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1994, no. 5, 23–28
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