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Mat. Sb., 2010, Volume 201, Number 1, Pages 103–128 (Mi msb6387)  

This article is cited in 9 scientific papers (total in 9 papers)

Topological transformation groups and Dugundji compacta

K. L. Kozlova, V. A. Chatyrkob

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

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.

DOI: https://doi.org/10.4213/sm6387

Full text: PDF file (656 kB)
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English version:
Sbornik: Mathematics, 2010, 201:1, 103–128

Bibliographic databases:

UDC: 515.122.4+515.122.536
MSC: Primary 54H15; Secondary 22A05, 54B15, 54D30, 54D35, 54E15
Received: 26.06.2008 and 03.07.2009

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

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. K. L. Kozlov, “Topology of actions and homogeneous spaces”, Sb. Math., 204:4 (2013), 588–620  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. K.L. Kozlov, “Spectral decompositions of spaces induced by spectral decompositions of acting groups”, Topology and its Applications, 160:11 (2013), 1188–1205  crossref  mathscinet  zmath  isi  scopus  scopus
    3. M. S. Shulikina, “Iterations of Resolvents and Homogeneous Cut-Point Spaces”, Math. Notes, 98:2 (2015), 316–324  mathnet  crossref  crossref  mathscinet  isi  elib
    4. Arhangel'skii A.V., “A Dichotomy Theorem and other results for a class of quotients of topological groups”, Topology Appl., 215 (2017), 1–10  crossref  mathscinet  zmath  isi  scopus
    5. E. Martyanov, “Characterization of $\Bbb R$-factorizable $G$-spaces”, Moscow University Mathematics Bulletin, 72:2 (2017), 49–54  mathnet  crossref  mathscinet  isi
    6. Kozlov K.L., “R-Factorizable G-Spaces”, Topology Appl., 227 (2017), 146–164  crossref  mathscinet  zmath  isi  scopus
    7. E. Martyanov, “Equiuniform Quotient Spaces”, Math. Notes, 104:6 (2018), 866–885  mathnet  crossref  crossref  isi  elib
    8. Whittington K., “The Sin Property in Homeomorphism Groups”, Topology Appl., 251 (2019), 94–106  crossref  mathscinet  zmath  isi  scopus
    9. E. Martyanov, “$\mathbb R$-factorizability of $G$-spaces in the category G-Tych”, Izv. Math., 83:2 (2019), 315–329  mathnet  crossref  crossref  adsnasa  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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