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. 
@article{IM2_2019_83_2_a7,
     author = {E. Martyanov},
     title = {$\mathbb R$-factorizability of $G$-spaces in the category {\textbf{G-Tych}}},
     journal = {Izvestiya. Mathematics },
     pages = {315--329},
     publisher = {mathdoc},
     volume = {83},
     number = {2},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2019_83_2_a7/}
}
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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/