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

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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.

作者简介

Evgeny Martyanov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Email: binom00@yandex.ru
without scientific degree, no status

参考

  1. A. Arhangel'skii, M. Tkachenko, Topological groups and related structures, Atlantis Stud. Math., 1, Atlantis Press, Paris; World Sci. Publ. Co. Pte. Ltd., Hackensack, NJ, 2008, xiv+781 pp.
  2. K. L. Kozlov, “$mathbb R$-factorizable $G$-spaces”, Topology Appl., 227 (2017), 146–164
  3. Е. В. Мартьянов, “Характеризация $mathbb R$-факторизуемых $G$-пространств”, Вестн. Моск. ун-та. Сер. 1. Матем., мех., 2017, № 2, 7–12
  4. R. Engelking, General topology, Transl. from the Polish, Sigma Ser. Pure Math., 6, 2nd ed., Hendermann Verlag, Berlin, 1989, viii+529 pp.
  5. J. R. Isbell, Uniform spaces, Math. Surveys Monogr., 12, Amer. Math. Soc., Providence, RI, 1964, xi+175 pp.
  6. W. Kulpa, “Factorization and inverse expansion theorems for uniformities”, Colloq. Math., 1970, no. 21, 217–227
  7. Е. В. Мартьянов, “Эквиравномерные факторпространства”, Матем. заметки, 104:6 (2018), 872–894
  8. M. G. Megrelishvili, “Compactification and factorization in the category of $G$-spaces”, Categorical topology and its relation to analysis, algebra and combinatorics (Prague, 1988), World Sci. Publ., Teaneck, NJ, 1989, 220–237
  9. J. De Vries, “On the existence of $G$-compactifications”, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys., 26:3 (1978), 275–280
  10. K. Л. Козлов, В. А. Чатырко, “О бикомпактных $G$-расширениях”, Матем. заметки, 78:5 (2005), 695–709
  11. V. A. Chatyrko, K. L. Kozlov, “The maximal $G$-compactifications of $G$-spaces with special actions”, Proceedings of the 9th Prague topological symposium (Prague, 2001), Topol. Atlas, North Bay, ON, 2002, 15–21
  12. J. de Vries, Topological transformation groups, v. 1, Math. Centre Tracts, 65, A categorical approach, Math. Centrum, Amsterdam, 1975, v+251 pp.
  13. М. Г. Мегрелишвили, “Тихоновское $G$-пространство, не обладающее бикомпактным $G$-расширением и $G$-линеаризацией”, УМН, 43:2(260) (1988), 145–146
  14. K. L. Kozlov, “Spectral decompositions of spaces induced by spectral decompositions of acting groups”, Topology Appl., 160:11 (2013), 1188–1205
  15. K. Л. Козлов, В. А. Чатырко, “Топологические группы преобразований и бикомпакты Дугунджи”, Матем. сб., 201:1 (2010), 103–128
  16. В. В. Успенский, “Компактные фактор-пространства топологических групп и спектры Хейдона”, Матем. заметки, 42:4 (1987), 594–602
  17. L. R. Ford, “Homeomorphism groups and coset spaces”, Trans. Amer. Math. Soc., 77 (1954), 490–497
  18. M. G. Megrelishvili, “Free topological $G$-groups”, New Zealand J. Math., 25:1 (1996), 59–72
  19. S. Antonyan, N. Antonyan, K. L. Kozlov, Coset spaces of metrizable groups
  20. M. Tkačenko, “Introduction to topological groups”, Topology Appl., 86:3 (1998), 179–231

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