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Extension of mappings from the product of pseudocompact spacesстатья
- Автор: Reznichenko Evgenii
- Журнал: Topology and its Applications
- Том: 322
- Год издания: 2022
- Издательство: Elsevier BV
- Местоположение издательства: Netherlands
- Первая страница: 108329
- DOI: 10.1016/j.topol.2022.108329
- Аннотация: Let X and Y be pseudocompact spaces and let the function Φ:X×Y→ℝ be separately continuous. The following conditions are equivalent: (1) there is a dense Gδ subset of D⊂Y so that Φ is continuous at every point of X×D (Namioka property); (2) Φ is quasicontinuous; (3) Φ extends to a separately continuous function on βX×βY. This theorem makes it possible to combine studies of the Namioka property and generalizations of the Eberlein-Grothendieck theorem on the precompactness of subsets of function spaces. We also obtain a characterization of separately continuous functions on the product of several pseudocompact spaces extending to separately continuous functions on products of Stone-Cech extensions of spaces. These results are used to study groups and Mal'tsev spaces with separately continuous operations.
- Добавил в систему: Резниченко Евгений Александрович