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Sharp bases and weakly uniform bases versus point-countable basesстатья
- Авторы: Arhangel'skii A.V., Just W., Rezniczenko E.A., Szeptycki P.J.
- Журнал: Topology and its Applications
- Том: 100
- Номер: 1
- Год издания: 2000
- Издательство: Elsevier BV
- Местоположение издательства: Netherlands
- Первая страница: 39
- Последняя страница: 46
- DOI: 10.1016/s0166-8641(98)00136-9
- Аннотация: A base for a topological space is said to be sharp if for every and every sequence of pairwise distinct elements of with for all the set forms a base at . Sharp bases of -spaces are weakly uniform. We investigate which spaces with sharp bases or weakly uniform bases have point-countable bases or are metrizable. In particular, Davis, Reed, and Wage had constructed in a 1976 paper a consistent example of a Moore space with weakly uniform base, but without a point-countable base. They asked whether such an example can be constructed in ZFC. We partly answer this question by showing that under CH, every first-countable space with a weakly uniform base and at most isolated points has a point-countable base.
- Добавил в систему: Резниченко Евгений Александрович