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Izv. RAN. Ser. Mat., 2019, Volume 83, Issue 2, Pages 126–141 (Mi izv8747)  

$\mathbb R$-factorizability of $G$-spaces in the category G-Tych

E. Martyanov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: 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.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-05369
This paper was written with the financial support of the Russian Foundation for Basic Research (grant no. 15-01-05369).


DOI: https://doi.org/10.4213/im8747

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English version:
Izvestiya: Mathematics, 2019, 83:2, 315–329

Bibliographic databases:

Document Type: Article
UDC: 515.122.4+515.122.536
MSC: 54H15, 54H11, 54E15
Received: 07.12.2017
Revised: 26.11.2018

Citation: E. Martyanov, “$\mathbb R$-factorizability of $G$-spaces in the category G-Tych”, Izv. RAN. Ser. Mat., 83:2 (2019), 126–141; Izv. Math., 83:2 (2019), 315–329

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  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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