R-factorizability of topological groups and G-spaces

In the present paper we investigate the relationship between R-factorizability of a G-space in the category G-Tych and R-factorizability of its acting group. We show that R-factorizability of an acting group with a d-open action doesn't imply for R-factorizability of a G-space. Transitivity of...

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Bibliographic Details
Published in:Topology and its applications 2023-04, Vol.329, p.108373, Article 108373
Main Author: Martyanov, E.V.
Format: Article
Language:English
Subjects:
G-space
G-Tychonov space
Topological group
Uniformity
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Summary:In the present paper we investigate the relationship between R-factorizability of a G-space in the category G-Tych and R-factorizability of its acting group. We show that R-factorizability of an acting group with a d-open action doesn't imply for R-factorizability of a G-space. Transitivity of a d-open action of R-factorizable group implies R-factorizability of a G-space in the category G-Tych. It is proven that if a d-openly acting group is openly factorizable, then the G-space is R-factorizable in the category G-Tych. Moreover, a σ-lattice of open homomorphisms on G induces a σ-lattice of equivariant d-open maps on (G,X,α) and X is an I-favorable space.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2022.108373