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Izvestiya: Mathematics, 2019, Volume 83, Issue 2, Pages 315–329
DOI: https://doi.org/10.1070/IM8747
(Mi im8747)
 

This article is cited in 4 scientific papers (total in 4 papers)

R-factorizability of G-spaces in the category G-Tych

E. Martyanov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
References:
Abstract: We introduce and characterize the notion of R-factorizability of G-spaces in the category G-Tych. For G-spaces with d-openly acting groups, we establish the equivalence of R-factorizability and R-factorizability in G-Tych. We prove the R-factorizability in G-Tych of every R-factorizable G-space with transitive action whose phase space possesses the Baire property. The Dieudonné completion of an R-factorizable group is shown to be the phase space of a G-space R-factorizable in G-Tych. We characterize R-factorizability in G-Tych under passage to the G-compactification.
Keywords: G-space, G-Tychonoff space, topological group, uniformity.
Funding agency Grant number
Russian Foundation for Basic Research 15-01-05369
This paper was written with the financial support of the Russian Foundation for Basic Research (grant no. 15-01-05369).
Received: 07.12.2017
Revised: 26.11.2018
Bibliographic databases:
Document Type: Article
UDC: 515.122.4+515.122.536
MSC: 54H15, 54H11, 54E15
Language: English
Original paper language: Russian
Citation: E. Martyanov, “R-factorizability of G-spaces in the category G-Tych”, Izv. Math., 83:2 (2019), 315–329
Citation in format AMSBIB
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\by E.~Martyanov
\paper $\mathbb R$-factorizability of $G$-spaces in the category \textbf{G-Tych}
\jour Izv. Math.
\yr 2019
\vol 83
\issue 2
\pages 315--329
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\crossref{https://doi.org/10.1070/IM8747}
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Linking options:
  • https://www.mathnet.ru/eng/im8747
  • https://doi.org/10.1070/IM8747
  • https://www.mathnet.ru/eng/im/v83/i2/p126
  • This publication is cited in the following 4 articles:
    1. E.V. Martyanov, “R-factorizability of topological groups and G-spaces”, Topology and its Applications, 329 (2023), 108373  crossref
    2. K.L. Kozlov, “Uniform equicontinuity and groups of homeomorphisms”, Topology and its Applications, 311 (2022), 107959  crossref
    3. E. V. Martyanov, “Conservation of factorizability of G-spaces by equivariant mappings”, Moscow University Mathematics Bulletin, 75:1 (2020), 34–37  mathnet  crossref  mathscinet  zmath  isi
    4. A. Karassev, K. L. Kozlov, “Admissible topologies for groups of homeomorphisms and substitutions of groups of g-spaces”, Topology Appl., 275 (2020), 107033  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:368
    Russian version PDF:48
    English version PDF:30
    References:46
    First page:9
     
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