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Nonnormality of remainders of some topological groupsстатья
- Авторы: Arhangel’skii A.V., van Mill J.
- Журнал: Comment. Math. Univ. Carolinae
- Том: 57
- Номер: 3
- Год издания: 2016
- Первая страница: 345
- Последняя страница: 352
- Аннотация: It is known that every remainder of a topological group is Lindelof pseudocompact. Motivated by this result, we study in this paper when a topological group G has a normal remainder. Here we continue this line of investigation, mainly for the case of precompact groups. We show that no pseudocompact group, whose weight is uncountable but less than c, has a normal remainder under MA+¬CH. We also show that if a precompact group with a countable network has a normal remainder, then this group is metrizable. We finally show that if Cp(X) has a normal remainder, then X is countable. This result provides us with many natural examples of topological groups all remainders of which are nonnormal.
- Добавил в систему: Архангельский Александр Владимирович