Geodesic
On extension of functions from countable subspaces
Funkcionalʹnyj analiz i ego priloženiâ, Tome 56 (2022) no. 4, pp. 35-42

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Three intermediate class of spaces $\mathscr{R}_1\subset \mathscr{R}_2\subset \mathscr{R}_3$ between the classes of $F$- and $\beta\omega$-spaces are considered. The $\mathscr{R}_1$- and $\mathscr{R}_3$-spaces are characterized in terms of the extension of functions. It is proved that the classes of $\mathscr{R}_1$-, $\mathscr{R}_2$-, $\mathscr{R}_3$-, and $\beta\omega$-spaces are not preserved by the Stone–Čech compactification.
Keywords: extremally disconnected space, $F$-space, countable subspace, $C^*$-embedded subspace, Stone–Čech compactification.
Mots-clés : $\mathscr{R}_1$-space, $\mathscr{R}_2$-space, $\mathscr{R}_3$-space 
@article{FAA_2022_56_4_a3,
     author = {A. Yu. Groznova},
     title = {On extension of functions from countable~subspaces},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {35--42},
     publisher = {mathdoc},
     volume = {56},
     number = {4},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2022_56_4_a3/}
}
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A. Yu. Groznova. On extension of functions from countable subspaces. Funkcionalʹnyj analiz i ego priloženiâ, Tome 56 (2022) no. 4, pp. 35-42. http://geodesic.mathdoc.fr/item/FAA_2022_56_4_a3/