This article is cited in 3 papers

Mathematics

Characterization of $\Bbb R$-factorizable $G$-spaces

E. Martyanov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: 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.

Key words: topological group, $G$-space, factorization, uniformity, $\mathrm{d}$-open action.

UDC: 515.122.4, 515.123

Received: 28.03.2016

 English version: Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 2017, 72:2, 49–54

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