On separately
somewhat-continuous functions (in Ukrainian)

O.V. Vitrenko; V.K. Maslyuchenko

It is proved that if $X$ is Baire, $Y$ second countable and $Z$ completely regular, then every separately somewhat continuous function $f:X\to Y$ is jointly somewhat nearly continuous and that this property is not true for functions $l^2_\alpha\to\Bbb R$ and $\Bbb Q^2\to\Bbb R$.

1. Kempisty S. Sur les fonctions quasicontinues // Fund. Math. 1932. V.19. P.184–197.

2. Frolik Z. Remarks concerning the invariance of Baire spaces under mappings // Czechoslovak. Math. J. 1961. V.11. P.381–385.

3. Ptak V. On the closed graph theorem // Czechoslovak. Math. J. 1959. V.9. P.523–527. (рос. переклад: Математика, 4:6(1960), 69–72).

4. Piotrowski Z. A survey of results concerning generalized continuity on topological spaces // Acta Math. Univ. Comen. 1987(88). 52. 53. P.91–110.

5. Бурбаки Н. Общая топология. Использование вещественных чисел в общей топологии. Функциональные пространства. Сводка результатов. – Москва: Наука, 1975. 408 с.

6. Энгелькинг Р. Общая топология. – Москва: Мир, 1986. 752 с. Чернiвецький державний унiверситет, каф. матем. аналiзу, Чернiвцi, 274031,

	On separately somewhat-continuous functions (in Ukrainian)
Author	O.V. Vitrenko, V.K. Maslyuchenko Department of Mathematical Analysis, Yuriy Fedkovych Chernivtsi National University, Chernivtsi 274031, Ukraine
Abstract	It is proved that if $X$ is Baire, $Y$ second countable and $Z$ completely regular, then every separately somewhat continuous function $f:X\to Y$ is jointly somewhat nearly continuous and that this property is not true for functions $l^2_\alpha\to\Bbb R$ and $\Bbb Q^2\to\Bbb R$.
Keywords	Baire space, second countable, completely regular
DOI	doi:10.30970/ms.6.1.113-118
Reference	1. Kempisty S. Sur les fonctions quasicontinues // Fund. Math. 1932. V.19. P.184–197. 2. Frolik Z. Remarks concerning the invariance of Baire spaces under mappings // Czechoslovak. Math. J. 1961. V.11. P.381–385. 3. Ptak V. On the closed graph theorem // Czechoslovak. Math. J. 1959. V.9. P.523–527. (рос. переклад: Математика, 4:6(1960), 69–72). 4. Piotrowski Z. A survey of results concerning generalized continuity on topological spaces // Acta Math. Univ. Comen. 1987(88). 52. 53. P.91–110. 5. Бурбаки Н. Общая топология. Использование вещественных чисел в общей топологии. Функциональные пространства. Сводка результатов. – Москва: Наука, 1975. 408 с. 6. Энгелькинг Р. Общая топология. – Москва: Мир, 1986. 752 с. Чернiвецький державний унiверситет, каф. матем. аналiзу, Чернiвцi, 274031,
Pages	113-118
Volume	6
Issue	1
Year	1996
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html

On separately somewhat-continuous functions (in Ukrainian)