Symmetrical quasicontinuity of joint quasicontinuous functions (in Ukrainian)

V.K. Maslyuchenko; V.V. Mykhajlyuk; V.V. Nesterenko

It is shown that if $X$ is a second countable space, $Y$ is either a second countable or metrizable space, $Z$ is a separable metrizable space and $f\colon X\times Y\to Z$ is a quasicontinuous map, then there is a residual subset $B$ of $Y$ such that $f$ is symmetrical quasicontinuous with respect to $y$ at every point of the product $X\times B$.

1. Маслюченко В.К., Нестеренко В.В. Горизонтальна квазінеперервність та її застосування. – Чернівці, 1996. – 15 c. – Деп. в УкрЎНТЕЎ 01.11.96, №98-Ук96.

2. Bögel K. Über partiell differenzierbare Funtionen Math. Z. – 1926. – S.490–498.

3. Breckenridge J.C., Nishiura T. Partial continuity, quasiconinuity and Baire spaces Bull. inst. Math. Acad. Sinica. – 1976. – V.4, №2. – P.191–203.

4. Martin N.F.G. Quasi-continuous functions on product spaces Duke Math. J. – 1961. – P.39–44.

5. Piotrowski Z. A survey of results concerning generalized continuity on topological spaces Acta Math. Univ. Comen. – 1987(88). – 194 52–53. – P.91–110.

6. Куратовский К. Топология, Т.1. – М.: Мир, 1966. – 594c.

7. Piotrowski Z. Quasi-continuity and product spaces Proc. Intern. Conf. Geam. Top., Warsaw., 1980. – P.349–352.

8. Вітренко О.В., Маслюченко В.К. Про ледь неперервні функції Матем. Студії. – 1996. – Т.6. – C.113–118.

9. Piotrowski Z. Separate and joint continuity Real Anal. Exch. – 1985–1986. – V.11, №2. – P.293–322.

	Symmetrical quasicontinuity of joint quasicontinuous functions (in Ukrainian)
Author	V.K. Maslyuchenko, V.V. Mykhajlyuk, V.V. Nesterenko Department of Mathematical Analysis, Yuriy Fedkovych Chernivtsi National University
Abstract	It is shown that if $X$ is a second countable space, $Y$ is either a second countable or metrizable space, $Z$ is a separable metrizable space and $f\colon X\times Y\to Z$ is a quasicontinuous map, then there is a residual subset $B$ of $Y$ such that $f$ is symmetrical quasicontinuous with respect to $y$ at every point of the product $X\times B$.
Keywords	second countable spaces, metrizable spaces, separable metrizable space, quasicontinuous maps, symmetrical quasicontinuity, residual subset, product of topological spaces
DOI	doi:10.30970/ms.11.2.204-208
Reference	1. Маслюченко В.К., Нестеренко В.В. Горизонтальна квазінеперервність та її застосування. – Чернівці, 1996. – 15 c. – Деп. в УкрЎНТЕЎ 01.11.96, №98-Ук96. 2. Bögel K. Über partiell differenzierbare Funtionen Math. Z. – 1926. – S.490–498. 3. Breckenridge J.C., Nishiura T. Partial continuity, quasiconinuity and Baire spaces Bull. inst. Math. Acad. Sinica. – 1976. – V.4, №2. – P.191–203. 4. Martin N.F.G. Quasi-continuous functions on product spaces Duke Math. J. – 1961. – P.39–44. 5. Piotrowski Z. A survey of results concerning generalized continuity on topological spaces Acta Math. Univ. Comen. – 1987(88). – 194 52–53. – P.91–110. 6. Куратовский К. Топология, Т.1. – М.: Мир, 1966. – 594c. 7. Piotrowski Z. Quasi-continuity and product spaces Proc. Intern. Conf. Geam. Top., Warsaw., 1980. – P.349–352. 8. Вітренко О.В., Маслюченко В.К. Про ледь неперервні функції Матем. Студії. – 1996. – Т.6. – C.113–118. 9. Piotrowski Z. Separate and joint continuity Real Anal. Exch. – 1985–1986. – V.11, №2. – P.293–322.
Pages	204-208
Volume	11
Issue	2
Year	1999
Journal	Matematychni Studii
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