New generalizations of Sierpinski theorem

V. K. Maslyuchenko; O. I. Filipchuk

doi:10.15330/ms.47.1.91-99

We introduce the notion of equi-feeblycontinuity which ressembles S. Kempisty's equi-quasicontinuity. Using this fresh notion and weak horizontal quasicontinuity, we obtain new generalizations of Sierpinski theorem on separately continuous functions.

1. Sierpinski W. Sur une propriete de fonctions de deux variables reelles, continues par rapport `a chacune de variables// Publ. Math. Univ. Belgrade. - 1932. - V.1. - P. 125-128.

2. Piotrowski Z., Wingler E.Y. On Sierpinskis theorem on the determination of separately continuous functions// Q&A in General Topology. - 1997. - V.15. - P. 15-19.

3. Tolstov G. On partial derivatives// Amer. Math. Soc. Transl., No. 69, Izv. Akad. Nauk SSSR Mat. - 1949. - V.13. - P. 425-449.

4. Marcus S. On functions continuous in each variable// Doklady Akad. Nauk SSSR. - 1957. - V.112. - P. 812-814.

5. Neugebauer C.J. A class of functions determined by dense sets// Archiv der Mathematik. - 1961. - V.12. - P. 206-209.

6. Goffman C., Neugebauer C.J. Linearly continuous functions// Proc. Amer. Math. Soc. - 1961. - V.12. - P. 997-998.

7. Comfort W.W. Functions linearly continuous on a product of Baire spaces// Boll. Un. Mat. Ital. - 1965. - V.20. - P. 128-134.

8. Mykhaylyuk V.V. Separate continuity topology and a generalization of Sierpinskis theorem// Math. Stud. - 2000. - V.14, №2. - P. 193-196. (in Ukrainian)

9. Maslyuchenko V.K., Filipchuk O.I. Discontinuity points of at most countable valued separately continuous mappings// Proc. of Int. Sci. Conf. Differential-functional equations and their applications, dedicated to the 80-th anniversary of M.P. Lenyuk (October, 28.30, 2016). - 2016. - P. 168-169. (in Ukrainian)

10. Maslyuchenko V.K., Filipchuk O.I. Discontinuity points of at most countable valued separately continuous mappings (to appear) (in Ukrainian)

11. Kempisty S. Sur les fonctions quasi-continues// Fund. Math. - 1932. - V.19. - P. 184-197.

12. Nesterenko V.V. Weak horizontal quasicontinuity// Math. Visn. NTSh. - 2008. - V.5. - P. 177-182. (in Ukrainian)

13. Maslyuchenko V.K. On separate and joint modifications of continuity// Mat. Stud. - 2006. - V.25, №2. - P. 213-218. (in Ukrainian)

14. Nesterenko V.V. On one characterization of joint quasicontinuity// Nauk. Visn. Cherniv. Univ., Mat. - 2007. - V.336-337. - P. 137-141. (in Ukrainian)

15. Haworth R.C., McCoy R.A. Baire spaces// Dis. Math. - 1977. - V.141. - P. 1-77.

16. Maslyuchenko V.K. Separately continuous mappings and Kothe spaces. Doctoral-Degree Thesis (Physics and Mathematics), Chernivtsi, 1999. - 345 p. (in Ukrainian)

	New generalizations of Sierpinski theorem(in Ukrainian)
Author	V. K. Maslyuchenko, O. I. Filipchuk v.maslyuchenko@gmail.com; o.filipchuk@chnu.edu.ua Chernivtsi National University, Chernivtsi, Ukraine
Abstract	We introduce the notion of equi-feeblycontinuity which ressembles S. Kempisty's equi-quasicontinuity. Using this fresh notion and weak horizontal quasicontinuity, we obtain new generalizations of Sierpinski theorem on separately continuous functions.
Keywords	Sierpinski theorem; separately continuous functions; equi-feeblycontinuity; weak horizontal quasicontinuity
DOI	doi:10.15330/ms.47.1.91-99
Reference	1. Sierpinski W. Sur une propriete de fonctions de deux variables reelles, continues par rapport `a chacune de variables// Publ. Math. Univ. Belgrade. - 1932. - V.1. - P. 125-128. 2. Piotrowski Z., Wingler E.Y. On Sierpinskis theorem on the determination of separately continuous functions// Q&A in General Topology. - 1997. - V.15. - P. 15-19. 3. Tolstov G. On partial derivatives// Amer. Math. Soc. Transl., No. 69, Izv. Akad. Nauk SSSR Mat. - 1949. - V.13. - P. 425-449. 4. Marcus S. On functions continuous in each variable// Doklady Akad. Nauk SSSR. - 1957. - V.112. - P. 812-814. 5. Neugebauer C.J. A class of functions determined by dense sets// Archiv der Mathematik. - 1961. - V.12. - P. 206-209. 6. Goffman C., Neugebauer C.J. Linearly continuous functions// Proc. Amer. Math. Soc. - 1961. - V.12. - P. 997-998. 7. Comfort W.W. Functions linearly continuous on a product of Baire spaces// Boll. Un. Mat. Ital. - 1965. - V.20. - P. 128-134. 8. Mykhaylyuk V.V. Separate continuity topology and a generalization of Sierpinskis theorem// Math. Stud. - 2000. - V.14, №2. - P. 193-196. (in Ukrainian) 9. Maslyuchenko V.K., Filipchuk O.I. Discontinuity points of at most countable valued separately continuous mappings// Proc. of Int. Sci. Conf. Differential-functional equations and their applications, dedicated to the 80-th anniversary of M.P. Lenyuk (October, 28.30, 2016). - 2016. - P. 168-169. (in Ukrainian) 10. Maslyuchenko V.K., Filipchuk O.I. Discontinuity points of at most countable valued separately continuous mappings (to appear) (in Ukrainian) 11. Kempisty S. Sur les fonctions quasi-continues// Fund. Math. - 1932. - V.19. - P. 184-197. 12. Nesterenko V.V. Weak horizontal quasicontinuity// Math. Visn. NTSh. - 2008. - V.5. - P. 177-182. (in Ukrainian) 13. Maslyuchenko V.K. On separate and joint modifications of continuity// Mat. Stud. - 2006. - V.25, №2. - P. 213-218. (in Ukrainian) 14. Nesterenko V.V. On one characterization of joint quasicontinuity// Nauk. Visn. Cherniv. Univ., Mat. - 2007. - V.336-337. - P. 137-141. (in Ukrainian) 15. Haworth R.C., McCoy R.A. Baire spaces// Dis. Math. - 1977. - V.141. - P. 1-77. 16. Maslyuchenko V.K. Separately continuous mappings and Kothe spaces. Doctoral-Degree Thesis (Physics and Mathematics), Chernivtsi, 1999. - 345 p. (in Ukrainian)
Pages	91-99
Volume	47
Issue	1
Year	2017
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html

New generalizations of Sierpinski theorem(in Ukrainian)