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Uspekhi Mat. Nauk, 1976, Volume 31, Issue 5(191), Pages 112–120 (Mi umn3959)  

This article is cited in 5 scientific papers (total in 5 papers)

On the dimension of spaces with a compact group of transformations

B. A. Pasynkov


Abstract: The main result of this paper is as follows:
{\it If a compact group $K$ acts continuously on a normal space $X$ so that the orbit space $X/K$ is metrizable, then $\dim X=\operatorname{Ind}X$}.
Particular cases of spaces on which a compact group acts continuously with a metrizable orbit space are locally compact groups and their quotient spaces and also almost metrizable (in particular, Čech-complete) groups [5] and their quotient spaces.
All the spaces we consider are assumed to be Hausdorff, and $X$ completely regular. All subgroups that occur are closed and all maps are continuous.

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English version:
Russian Mathematical Surveys, 1976, 31:5, 128–137

Bibliographic databases:

UDC: 513.83
MSC: 57S10, 22Exx, 57S15, 54E50
Received: 12.04.1976

Citation: B. A. Pasynkov, “On the dimension of spaces with a compact group of transformations”, Uspekhi Mat. Nauk, 31:5(191) (1976), 112–120; Russian Math. Surveys, 31:5 (1976), 128–137

Citation in format AMSBIB
\Bibitem{Pas76}
\by B.~A.~Pasynkov
\paper On~the~dimension of~spaces with a~compact group of~transformations
\jour Uspekhi Mat. Nauk
\yr 1976
\vol 31
\issue 5(191)
\pages 112--120
\mathnet{http://mi.mathnet.ru/umn3959}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=445470}
\zmath{https://zbmath.org/?q=an:0343.54031|0355.54026}
\transl
\jour Russian Math. Surveys
\yr 1976
\vol 31
\issue 5
\pages 128--137
\crossref{https://doi.org/10.1070/RM1976v031n05ABEH004193}


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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. B. A. Pasynkov, “Factorization theorems in dimension theory”, Russian Math. Surveys, 36:3 (1981), 175–209  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. S. M. Ageev, “Equivariant classification of continuous functions on $G$-spaces”, Russian Math. Surveys, 39:4 (1984), 111–112  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. V. V. Fedorchuk, “The Urysohn identity and dimension of manifolds”, Russian Math. Surveys, 53:5 (1998), 937–974  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    4. Sergey A. Antonyan, Hugo Juárez-Anguiano, “Dimension of proper G-spaces”, Topology and its Applications, 2011  crossref
    5. I. M. Leibo, “On the Dimension of Preimages of Certain Paracompact Spaces”, Math. Notes, 103:3 (2018), 405–414  mathnet  crossref  crossref  isi  elib
  • Успехи математических наук Russian Mathematical Surveys
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