$\mathbb R$-factorizability of $G$-spaces in the category G-Tych
- Authors: Martyanov E.V.1
-
Affiliations:
- Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
- Issue: Vol 83, No 2 (2019)
- Pages: 126-141
- Section: Articles
- URL: https://journals.rcsi.science/1607-0046/article/view/142309
- DOI: https://doi.org/10.4213/im8747
- ID: 142309
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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 spacepossesses the Baire property. The Dieudonne completion of an$\mathbb R$-factorizable group is shown to be the phase spaceof a $G$-space $\mathbb R$-factorizable in G-Tych. We characterize$\mathbb R$-factorizability in G-Tych under passageto the $G$-compactification.
Keywords
About the authors
Evgeny Vyacheslavovich Martyanov
Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Email: binom00@yandex.ru
without scientific degree, no status
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