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Grothendieck’s Theorem on the Precompactness of Subsets of Functional Spaces over Pseudocompact Spacesстатья Исследовательская статья
- Автор: Reznichenko Evgenii
- Журнал: Functional Analysis and its Applications
- Том: 58
- Номер: 4
- Год издания: 2024
- Издательство: Maik Nauka/Interperiodica Publishing
- Местоположение издательства: Russian Federation
- Первая страница: 409
- Последняя страница: 426
- DOI: 10.1134/s0016266324040051
- Аннотация: Generalizations of the theorems of Eberlein and Grothendieck on the precompactness of subsets of function spaces are considered: if is a countably compact space and is a space of continuous functions on in the topology of pointwise convergence, then any countably compact subspace of the space is precompact, that is, it has a compact closure. The paper provides an overview of the results on this topic. It is proved that if a pseudocompact X contains a dense Lindelöf \Sigma-space, then pseudocompact subspaces of the space C_p(X) are precompact. If X is the product Čech complete spaces, then bounded subsets of the space C_p(X) are precompact. Results on the continuity of separately continuous functions are also obtained.
- Добавил в систему: Резниченко Евгений Александрович