Geodesic
$\mathbb R$-factorizability of $G$-spaces in the category \textbf{G-Tych}
Izvestiya. Mathematics , Tome 83 (2019) no. 2, pp. 315-329.

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We introduce and characterize the notion of $\mathbb R$-factorizability of $G$-spaces in the category G-Tych. For $G$-spaces with $d$-openly acting groups, we establish the equivalence of $\mathbb R$-factorizability and $\mathbb R$-factorizability in G-Tych. We prove the $\mathbb R$-factorizability in G-Tych of every $\mathbb R$-factorizable $G$-space with transitive action whose phase space possesses the Baire property. The Dieudonné completion of an $\mathbb R$-factorizable group is shown to be the phase space of a $G$-space $\mathbb R$-factorizable in G-Tych. We characterize $\mathbb R$-factorizability in G-Tych under passage to the $G$-compactification.
Keywords: $G$-space, $G$-Tychonoff space, topological group, uniformity. 
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E. Martyanov. $\mathbb R$-factorizability of $G$-spaces in the category \textbf{G-Tych}. Izvestiya. Mathematics , Tome 83 (2019) no. 2, pp. 315-329. http://geodesic.mathdoc.fr/item/IM2_2019_83_2_a7/

[1] A. Arhangel'skii, M. Tkachenko, Topological groups and related structures, Atlantis Stud. Math., 1, Atlantis Press, Paris; World Sci. Publ. Co. Pte. Ltd., Hackensack, NJ, 2008, xiv+781 pp. | DOI | MR | Zbl

[2] K. L. Kozlov, “$\mathbb R$-factorizable $G$-spaces”, Topology Appl., 227 (2017), 146–164 | DOI | MR | Zbl

[3] E. V. Martyanov, “Characterization of $\mathbb R$-factorizable $G$-spaces”, Moscow Univ. Math. Bull., 72:2 (2017), 49–54 | DOI | MR | Zbl

[4] R. Engelking, General topology, Transl. from the Polish, Sigma Ser. Pure Math., 6, 2nd ed., Hendermann Verlag, Berlin, 1989, viii+529 pp. | MR | Zbl

[5] J. R. Isbell, Uniform spaces, Math. Surveys Monogr., 12, Amer. Math. Soc., Providence, RI, 1964, xi+175 pp. | MR | Zbl

[6] W. Kulpa, “Factorization and inverse expansion theorems for uniformities”, Colloq. Math., 1970, no. 21, 217–227 | DOI | MR | Zbl

[7] E. V. Martyanov, “Ekviravnomernye faktorprostranstva”, Matem. zametki, 104:6 (2018), 872–894 | DOI | MR

[8] M. G. Megrelishvili, “Compactification and factorization in the category of $G$-spaces”, Categorical topology and its relation to analysis, algebra and combinatorics (Prague, 1988), World Sci. Publ., Teaneck, NJ, 1989, 220–237 | MR

[9] J. De Vries, “On the existence of $G$-compactifications”, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys., 26:3 (1978), 275–280 | MR | Zbl

[10] K. L. Kozlov, V. A. Chatyrko, “On $G$-compactifications”, Math. Notes, 78:5 (2005), 649–661 | DOI | DOI | MR | Zbl

[11] V. A. Chatyrko, K. L. Kozlov, “The maximal $G$-compactifications of $G$-spaces with special actions”, Proceedings of the 9th Prague topological symposium (Prague, 2001), Topol. Atlas, North Bay, ON, 2002, 15–21 | MR | Zbl

[12] J. de Vries, Topological transformation groups, v. 1, Math. Centre Tracts, 65, A categorical approach, Math. Centrum, Amsterdam, 1975, v+251 pp. | MR | Zbl

[13] M. G. Megrelishvili, “A Tikhonov $G$-space not admitting a compact Hausdorff $G$-extension or $G$-linearization”, Russian Math. Surveys, 43:2 (1988), 177–178 | DOI | MR | Zbl

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

[15] K. L. Kozlov, V. A. Chatyrko, “Topological transformation groups and Dugundji compacta”, Sb. Math., 201:1 (2010), 103–128 | DOI | DOI | MR | Zbl

[16] V. V. Uspenskii, “Compact factor spaces of topological groups and Haydon spectra”, Math. Notes, 42:4 (1987), 827–831 | DOI | MR | Zbl

[17] L. R. Ford, “Homeomorphism groups and coset spaces”, Trans. Amer. Math. Soc., 77 (1954), 490–497 | DOI | MR | Zbl

[18] M. G. Megrelishvili, “Free topological $G$-groups”, New Zealand J. Math., 25:1 (1996), 59–72 | MR | Zbl

[19] S. Antonyan, N. Antonyan, K. L. Kozlov, Coset spaces of metrizable groups, arXiv: 1711.10015

[20] M. Tkačenko, “Introduction to topological groups”, Topology Appl., 86:3 (1998), 179–231 | DOI | MR | Zbl