On extension of functions from countable subspaces

A. Yu. Groznova

Lomonosov Moscow State University

Abstract: 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, $\mathscr{R}_1$-space, $\mathscr{R}_2$-space, $\mathscr{R}_3$-space, countable subspace, $C^*$-embedded subspace, Stone–Čech compactification.

UDC: 515.12

Received: 27.07.2022
Revised: 11.09.2022
Accepted: 19.09.2022

DOI: 10.4213/faa4038

 English version: Functional Analysis and Its Applications, 2022, 56:4, 264–268

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