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Discrete subsets in topological groups and countable extremally disconnected groupsстатья Исследовательская статья
Информация о цитировании статьи получена из
Web of Science,
Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 7 июля 2021 г.
- Авторы: Reznichenko E., Sipacheva O.
- Журнал: Proceedings of the American Mathematical Society. American Mathematical Society
- Том: 149
- Номер: 6
- Год издания: 2021
- Издательство: American Mathematical Society.
- Местоположение издательства: [Providence, R.I., etc.], United States
- Первая страница: 2655
- Последняя страница: 2668
- DOI: 10.1090/proc/13992
- 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. We also prove that any countabletopological group in which the filter of neighborhoods of the identity elementis not rapid contains a discrete set with precisely one limit point, which gives anegative answer to Protasov’s question on the existence in ZFC of a countablenondiscrete group in which all discrete subsets are closed.
- Добавил в систему: Сипачева Ольга Викторовна