Compactification of spaces of measures and pseudocompactness

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Abstract

We prove pseudocompactness of a Tychonoff space X and the space P(X) of Radon probability measures on it with the weak topology under the condition that the Stone–ech compactification of the space P(X) is homeomorphic to the space P(βX) of Radon probability measures on the Stone–ech compactification of the space X.

About the authors

V. I. Bogachev

Moscow State Lomonosov University; National Research University Higher School of Economics; Saint-Tikhon's Orthodox University; Moscow Center of Fundamental and Applied Mathematics

Author for correspondence.
Email: vibogach@mail.ru

Corresponding Member of the RAS

Russian Federation, Moscow; Moscow; Moscow; Moscow

References

  1. Богачев В.И. // Функц. анал. и его прил. 2024. Т. 58. № 1. С. 4–21.
  2. Bogachev V.I. Measure theory. V. 2. Springer, New Your, 2007.
  3. Bogachev V.I. Weak convergence of measures. Amer. Math. Soc., Providence, Rhode Island, 2018.
  4. Banaschewski B. // Canadian J. Math. 1956. V. 8. P. 395–398.
  5. Henriksen M., Isbell J.R. // Illinois J. Math. 1957. V. 1. P. 574–582.
  6. Walker R.C. The Stone-Čech compactification. Springer-Verlag, Berlin – New York, 1974.
  7. Colmez J. // C. R. Acad. Paris. 1952. T. 234. P. 1019–1921.
  8. Angoa-Amador J., Contreras-Carreto A., Ibarra-Contreras M., Tamariz-Mascarúa A. Basic and classic results on pseudocompact spaces. In: Pseudocompact topological spaces. A survey of classic and new results with open problems. Edited by Michael Hrušák, Ángel Tamariz-Mascarúa and Mikhail Tkachenko. Developments in Mathematics, 55, pp. 1–38, Springer, Cham, 2018.
  9. Koumoullis G. // Adv. Math. 1996. V. 124. № 1. P. 1–24.
  10. Wójcicka M. // Bull. Polish Acad. Sci. Math. 1985. V. 33. P. 305–311.
  11. Dorantes-Aldama A., Okunev O., Tamariz-Mascarúa Á. Weakly pseudocompact spaces. In: Pseudocompact topological spaces. A survey of classic and new results with open problems. Edited by Michael Hrušák, Ángel Tamariz-Mascarúa and Mikhail Tkachenko. Developments in Mathematics, 55, pp. 151–190, Springer, Cham, 2018.
  12. Brown J.B. // Fund. Math. 1977. V. 96. P. 189–193.
  13. Brown J.B., Cox G.V. // Fund. Math. 1984. V. 121. P. 143–148.
  14. Krupski M. // J. Inst. Math. Jussieu. 2022. V. 21. № 3. P. 851–868.
  15. Koumoullis G., Sapounakis A. // Mich. Math. J. 1984. V. 31. № 1. P. 31–47.
  16. Архангельский А.В., Пономарев В.И. Основы общей топологии в задачах и упражнениях. Наука, М., 1974.
  17. Vaughan J.E. Countably compact and sequentially compact spaces. In: Handbook of set-theoretic topology, pp. 569–602, North-Holland, Amsterdam, 1984.
  18. Gillman L., Jerison M. Rings of continuous functions. Van Nostrand, Princeton – New York, 1960.
  19. van Mill J. An introduction to βω. In: Handbook of set-theoretic topology, pp. 503–567, North-Holland, Amsterdam, 1984.
  20. Szymański A. // Colloq. Math. 1977. V. 37. P. 185–192.
  21. Wimmers E. // Israel J. Math. 1982. V. 43. № 1. P. 28–48.
  22. Энгелькинг Р. Общая топология. Мир, М., 1986.
  23. Hernández-Hernández F., Hrušák M. Topology of Mrówka-Isbell spaces. In: Pseudocompact topological spaces. A survey of classic and new results with open problems. Edited by Michael Hrušák, Ángel Tamariz-Mascarúa and Mikhail Tkachenko. Developments in Mathematics, 55, pp. 253–289, Springer, Cham, 2018.
  24. Lipecki Z. // Colloq. Math. 2011. V. 123. № 1. P. 133–147.

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