K. L. Kozlov, V. A. Chatyrko, “Topological transformation groups and Dugundji compacta”, Sb. Math., 201:1 (2010), 103

Sbornik: Mathematics

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Sbornik: Mathematics, 2010, Volume 201, Issue 1, Pages 103–128
DOI: https://doi.org/10.1070/SM2010v201n01ABEH004067 (Mi sm6387)

This article is cited in 21 scientific papers (total in 21 papers)

Topological transformation groups and Dugundji compacta

K. L. Kozlov^a, V. A. Chatyrko^b

^a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
^b Linköping University

English version PDF (417 kB) Citations (21) Russian version article

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DOI: https://doi.org/10.1070/SM2010v201n01ABEH004067

Abstract: The presence of an algebraic structure on a space, which is compatible with its topology, in many cases imposes very strong restrictions on the properties of the space itself. Conditions are found which must be satisfied by the actions in order for the phase space to be a $d$-space (Dugundji compactum). This investigation allows the range of $G$-spaces that are $d$-spaces (Dugundji compacta) to be substantially widened. It is shown that all the cases known to the authors where a $G$-space (a topological group, one of its quotient spaces) is a $d$-space can be realized using equivariant maps.
Bibliography: 39 titles.

Keywords: $G$-space, topological group, Dugundji compactum, $d$-space, uniform structure.

Received: 26.06.2008 and 03.07.2009

Bibliographic databases:

UDC: 515.122.4+515.122.536

MSC: Primary 54H15; Secondary 22A05, 54B15, 54D30, 54D35, 54E15

Language: English

Original paper language: Russian

Citation: K. L. Kozlov, V. A. Chatyrko, “Topological transformation groups and Dugundji compacta”, Sb. Math., 201:1 (2010), 103–128

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Linking options:

https://www.mathnet.ru/eng/sm6387

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https://www.mathnet.ru/eng/sm/v201/i1/p103

This publication is cited in the following 21 articles:

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A. A. Zaitov, D. T. Eshkobilova, “Dugundji Compacta and the Space of Idempotent Probability Measures”, Math. Notes, 114:4 (2023), 433–442
Piyu Li, Lei Mou, Rongxin Shen, Yanqin Xu, “Two questions on coset spaces of semitopological groups”, Topology and its Applications, 338 (2023), 108667
Michael Megrelishvili, “Maximal equivariant compactifications”, Topology and its Applications, 329 (2023), 108372
E.V. Martyanov, “R-factorizability of topological groups and G-spaces”, Topology and its Applications, 329 (2023), 108373
Antonyan S. Antonyan N. Kozlov K.L., “Coset Spaces of Metrizable Groups”, Colloq. Math., 2022
K.L. Kozlov, “Uniform equicontinuity and groups of homeomorphisms”, Topology and its Applications, 311 (2022), 107959
E. V. Martyanov, “Conservation of factorizability of $G$-spaces by equivariant mappings”, Moscow University Mathematics Bulletin, 75:1 (2020), 34–37
Cabello Sanchez F., Dantas Sh., Kadets V., Kim S.K., Lee H.J., Martin M., “On Banach Spaces Whose Group of Isometrics Acts Micro-Transitively on the Unit Sphere”, J. Math. Anal. Appl., 488:1 (2020), 124046
Karassev A. Kozlov K.L., “Admissible Topologies For Groups of Homeomorphisms and Substitutions of Groups of G-Spaces”, Topology Appl., 275 (2020), 107033
Whittington K., “The Sin Property in Homeomorphism Groups”, Topology Appl., 251 (2019), 94–106
E. Martyanov, “$\mathbb R$-factorizability of $G$-spaces in the category G-Tych”, Izv. Math., 83:2 (2019), 315–329
van Mill J., Valov V.M., “Actions of Semitopological Groups”, Can. Math. Bul.-Bul. Can. Math., 62:2 (2019), 441–450
E. Martyanov, “Equiuniform Quotient Spaces”, Math. Notes, 104:6 (2018), 866–885
N. Antonyan, S. Antonyan, M. Sanchis, Developments in Mathematics, 55, Pseudocompact Topological Spaces, 2018, 217
Arhangel'skii A.V., “A Dichotomy Theorem and other results for a class of quotients of topological groups”, Topology Appl., 215 (2017), 1–10
E. Martyanov, “Characterization of $\Bbb R$-factorizable $G$-spaces”, Moscow University Mathematics Bulletin, 72:2 (2017), 49–54
Kozlov K.L., “R-Factorizable G-Spaces”, Topology Appl., 227 (2017), 146–164
M. S. Shulikina, “Iterations of Resolvents and Homogeneous Cut-Point Spaces”, Math. Notes, 98:2 (2015), 316–324
K. L. Kozlov, “Topology of actions and homogeneous spaces”, Sb. Math., 204:4 (2013), 588–620

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

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Abstract page:	1030
Russian version PDF:	308
English version PDF:	34
References:	100
First page:	27

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