Geodesic
Characterization of $\Bbb R$-factorizable $G$-spaces
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2017), pp. 7-12 
E. Martyanov. Characterization of $\Bbb R$-factorizable $G$-spaces. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2017), pp. 7-12. http://geodesic.mathdoc.fr/item/VMUMM_2017_2_a1/
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     title = {Characterization of $\Bbb R$-factorizable $G$-spaces},
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we characterize $\mathbb R$-factorizability of $G$-spaces and prove the equivalence of $\mathbb R$-factorizability and $\omega$-$U$ property for $G$-spaces with $\mathrm{d}$-open actions of $\omega$-narrow groups. It is shown that the $\mathbb R$-factorizability characterizes those compact coset spaces which are coset spaces of $\omega$-narrow groups. The notion of $m$- and $M$-factorizable $G$-spaces is introduced, which generalizes the corresponding notions for topological groups.

[1] Arhangel'skii A.V., Tkachenko M.G., Topological groups and related structures, Atlantis Press, Paris, 2008 | MR | Zbl

[2] Tkachenko M.G., “Factorization theorems for topological groups and their applications”, Topol. and Appl., 38:1 (1991), 21–37 | DOI | MR | Zbl

[3] Xie L.H., Lin S., “$\mathbb R$" factorizability and uniform continuity in topological groups”, Topol. and Appl., 159:11–12 (2012), 2711–2720 | DOI | MR | Zbl

[4] Kozlov K.L., “$\mathbb R$" factorizable $G$" spaces”, Topol. and Appl., 2017 | DOI | MR

[5] Uspenskii V.V., “Topologicheskie gruppy i kompakty Dugundzhi”, Matem. sb., 180:8 (1989), 103–128

[6] Engelking R., Per. s angl., Mir, M., 1986 | MR

[7] Kozlov K.L., “Spectral decompositions of spaces induced by spectral decompositions of acting groups”, Topol. and Appl., 160:11 (2013), 1188–1205 | DOI | MR | Zbl

[8] Kozlov K.L., Chatyrko V.A., “Topologicheskie gruppy preobrazovanii i kompakty Dugundzhi”, Matem. sb., 201:1 (2010), 103–128 | DOI | MR | Zbl