Geodesic
On the Homogeneity of Products of Topological Spaces
Matematičeskie zametki, Tome 113 (2023) no. 2, pp. 171-181

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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.
Mots-clés : $\mathscr R_1$-space, $\mathscr R_2$-space, $\mathscr R_3$-space, NNCPP$_\kappa$
Keywords: Rudin–Keisler order, Rudin–Blass order, $\beta\omega$-space, homogeneity of products of topological spaces. 
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     author = {A. Yu. Groznova},
     title = {On the {Homogeneity} of {Products} of {Topological} {Spaces}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {171--181},
     publisher = {mathdoc},
     volume = {113},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2023_113_2_a1/}
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A. Yu. Groznova. On the Homogeneity of Products of Topological Spaces. Matematičeskie zametki, Tome 113 (2023) no. 2, pp. 171-181. http://geodesic.mathdoc.fr/item/MZM_2023_113_2_a1/