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Completeness and reflexivity type properties of B₁(X)статья
- Авторы: Gabriyelyan Saak, Osipov Alexander, Reznichenko Evgenii
- Журнал: ArXiv e-prints
- Год издания: 2026
- Первая страница: 1
- Последняя страница: 17
- DOI: 10.48550/ARXIV.2601.00733
- Аннотация: For a Tychonoff space X, B1(X) denotes the space of all Baire-one functions on X endowed with the pointwise topology. We prove that the following assertions are equivalent: (1) B1(X) is a (semi-)Montel space, (2) B1(X) is a (semi-)reflexive space, (3) B1(X) is a (quasi-)complete space, (4) B1(X)=ℝX, (5) X is a Qf-space. It is proved that B1(X) is sequentially complete iff B1(X) is locally complete iff X is a CZ-space. In the case when K is a compact space, we show that B1(K) is locally complete iff K is scattered. We thoroughly study the case when X is a separable metrizable space. Numerous distinguished examples are given.
- Добавил в систему: Резниченко Евгений Александрович