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Homogeneous Subspaces of Products of Extremally Disconnected Spacesстатья
- Автор: Reznichenko Evgenii
- Журнал: Topology and its Applications
- Том: 284
- Год издания: 2020
- Издательство: Elsevier BV
- Местоположение издательства: Netherlands
- Первая страница: 107403
- DOI: 10.1016/j.topol.2020.107403
- Аннотация: Homogeneous countably compact spaces X and Y whose product X×Y is not pseudocompact are constructed. It is proved that all compact subsets of homogeneous subspaces of the third power of an extremally disconnected space are finite. Moreover, under CH, all compact subsets of homogeneous subspaces of any finite power of an extremally disconnected space are finite and all compact subsets of homogeneous subspaces of the countable power of an extremally disconnected space are metrizable. It is also proved that all compact homogeneous subspaces of finite powers of an extremally disconnected space are finite, which strengthens Frolík's theorem.
- Добавил в систему: Резниченко Евгений Александрович