Abstract
Three intermediate classes \(\mathscr R_1\subset\mathscr R_2\subset\mathscr R_3\) between the classes of \(F\)-spaces and of \(\beta\omega\)-spaces are considered. It is proved that products of infinite \(\mathscr R_2\)-spaces and, under the assumption of the existence of a discrete ultrafilter, of infinite \(\beta\omega\)-spaces are never homogeneous. Under additional set-theoretic assumptions, the metrizability of any compact subspace of a countable product of homogeneous \(\beta\omega\)-spaces is proved.
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Acknowledgments
The author expresses deep gratitude to her scientific advisor Ol’ga Viktorovna Sipacheva for setting the problem, many useful discussions, and patience, to Evgenii Aleksandrovich Reznichenko for stimulating discussions, and to the referee for valuable comments.
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Translated from Matematicheskie Zametki, 2023, Vol. 113, pp. 171–181 https://doi.org/10.4213/mzm13634.
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Groznova, A.Y. On the Homogeneity of Products of Topological Spaces. Math Notes 113, 182–190 (2023). https://doi.org/10.1134/S0001434623010212
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DOI: https://doi.org/10.1134/S0001434623010212