Connected three-point and first-class Baire functions

Karlova Olena; Mykhaylyuk Volodymyr

Karlova Olena ^1,2 , Mykhaylyuk Volodymyr ^1,2

¹ Department of Mathematical Analysis, Yuriy Fedkovych Chernivtsi National University, Chernivtsi, 58000, Ukraine

² Jan Kokhanowski University, Kielce, 25-001, Poland

Keywords: connected three-point, the first Baire class

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Abstract

We prove that every separately continuous function, defined on a product of the real line and a topological space with values in an equiconnected space belongs to the first Baire class.

References

[1] Lebesgue, H. Sur l’approximation des fonctions / / Bull. Sei. Math. - 1898. - 22. - P. 278 - 287.

[2] Moran, W . Separate continuity and supports of measures / / J. London Math. Soe. - 1969. - 44. - P. 320 - 324.

[3] Vera, G. Baire mesurability f separately continuous functions / / Quart. J. Math. Oxford (2). - 1988. - 39. - P. 109 - 116.

[4] Rudin, W . Lebesgue first theorem / / Math. Analysis and Applications, Part B. Edited by Nachbin. Adv. in Math. Supplem. Studies 78. - Academic Press, 1981. - P. 741 - 747.

[5] Maslyuchenko V.K., Sobchuk O.V. Beres classification and $σ$-metric spaces // Mat. - 1994. - 3. - P. 95 - 101.

[6] Kalancha A.K., Maslyuchenko V.K. Lebesgue-Cheh dimension and Baire classification of vector-valued separately continuous mappings // Ukrainian Math. - 2003. - 55, № 11. - P. 1596 - 1599.

[7] Banakh Т.О. (Metrically) quarter-stratifiable spaces and their applications / / Мат. студії. - 18, № 1. - С. 10 - 28. - 2002.

[8] Karlova O.O., Maslyuchenko V.K. Separately continuous mappings with values in non-locally convex spaces // Ukrainian Mathematical Journal - 2007. - Vol. 59, № 12, p. 1639 - 1646.

[9] Karlova O.O. Separately continuous $σ$-discrete mappings // Scientific Bulletin of Chernivtsi Univ. Iss. 314 - 315. Mathematics. - Chernivtsi: Ruta, 2006. - P.77- 79.

[10] R. Engelking, General Topology. Revised and completed edition. Heldermann Verlag, Berlin (1989).

[11] Kuratoweki K. Topology. - T.l. - Moscow: Mir, 1966. - 596 p.

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Cite

ACS Style: Karlova, O.; Mykhaylyuk, V. Connected three-point and first-class Baire functions. Bukovinian Mathematical Journal. 2018, 1
AMA Style: Karlova O, Mykhaylyuk V. Connected three-point and first-class Baire functions. Bukovinian Mathematical Journal. 2018; 1(4).
Chicago/Turabian Style: Olena Karlova, Volodymyr Mykhaylyuk. 2018. "Connected three-point and first-class Baire functions". Bukovinian Mathematical Journal. 1 no. 4.

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