Construction of a separately continuous function with given oscillation
We investigate the problem of construction of a separately continuous function f whose oscillation is equal to a given nonnegative function g. We show that, in the case of a metrizable Baire product, the problem under consideration is solvable if and only if g is upper semicontinuous and its support...
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| Дата: | 1998 |
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| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Українська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
1998
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/4875 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | We investigate the problem of construction of a separately continuous function f whose oscillation is equal to a given nonnegative function g. We show that, in the case of a metrizable Baire product, the problem under consideration is solvable if and only if g is upper semicontinuous and its support can be covered by countably many sets, which are locally contained in products of sets of the first category. |
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