Reznichenko E., Sipacheva O. Discrete subsets in topological groups and countable extremally disconnected groups // Proceedings of the American Mathematical Society. American Mathematical Society. — 2021. — Vol. 149, no. 6. — P. 2655–2668.
Аннотация
In 1967 Arhangel’skii posed the problem of the existence in ZFCof a nondiscrete extremally disconnected topological group. The general caseis still open, but we solve Arhangel’skii’s problem for the class of countablegroups. Namely, we prove that the existence of a countable nondiscrete ex-tremally disconnected group implies the existence of a rapid ultrafilter; hence,such a group cannot be constructed in ZFC.