Abstract:
We introduce and characterize the notion of R-factorizability
of G-spaces in the category G-Tych.
For G-spaces with d-openly acting groups,
we establish the equivalence of R-factorizability and
R-factorizability in G-Tych. We prove the
R-factorizability in G-Tych of every
R-factorizable G-space with transitive action whose phase space
possesses the Baire property. The Dieudonné completion of an
R-factorizable group is shown to be the phase space
of a G-space R-factorizable in G-Tych. We characterize
R-factorizability in G-Tych under passage
to the G-compactification.
This publication is cited in the following 4 articles:
E.V. Martyanov, “R-factorizability of topological groups and G-spaces”, Topology and its Applications, 329 (2023), 108373
K.L. Kozlov, “Uniform equicontinuity and groups of homeomorphisms”, Topology and its Applications, 311 (2022), 107959
E. V. Martyanov, “Conservation of factorizability of G-spaces by equivariant mappings”, Moscow University Mathematics Bulletin, 75:1 (2020), 34–37
A. Karassev, K. L. Kozlov, “Admissible topologies for groups of homeomorphisms and substitutions of groups of g-spaces”, Topology Appl., 275 (2020), 107033