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

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

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
2. S. M. Ageev, “Equivariant classification of continuous functions on $G$-spaces”, Russian Math. Surveys, 39:4 (1984), 111–112
3. V. V. Fedorchuk, “The Urysohn identity and dimension of manifolds”, Russian Math. Surveys, 53:5 (1998), 937–974
4. Sergey A. Antonyan, Hugo Juárez-Anguiano, “Dimension of proper G-spaces”, Topology and its Applications, 2011
5. I. M. Leibo, “On the Dimension of Preimages of Certain Paracompact Spaces”, Math. Notes, 103:3 (2018), 405–414
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