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Baire classification of discretely continuous functions and dependence on a countable number of coordinates
Mykhaylyuk Volodymyr 1,2 , Sobchuk Oleksandr Vasyliovych 3
1 Department of Mathematical Analysis, Yuriy Fedkovych Chernivtsi National University, Chernivtsi, 58000, Ukraine
2 Jan Kokhanowski University, Kielce, 25-001, Poland
3 Professional College of Yuriy Fedkovych Chernivtsi National University, Chernivtsi , 58000, Ukraine
Keywords: Baire classification, discretely continuous functions
Abstract

It is proved that any separately continuous function $f: X × Y → \mathbb{R}$ is Baire one if $X$ is a separable space and $Y$ is a Lindelöf pseudocompact or $X$ satisfies condition $(I I_{\aleph _0})$ and $Y$ is a Valdivia compact.

References

[1] Lebesgue H. Sur les fonctions représentables analitiquement // Journ. de Math., ser.2. - 1905. - 1 . - P.139-216.

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

[3] Vera G. Baire measurability of separately continuous functions // Quart. J. Math. Oxford(2). - 39, N 153. - 1988. - P.109-116.

[4] Engelking R. General topology. - M.: Mir, 1986. - 752 p.

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

Cite
ACS Style
Mykhaylyuk, V.; Sobchuk, O.V. Baire classification of discretely continuous functions and dependence on a countable number of coordinates. Bukovinian Mathematical Journal. 2018, 1
AMA Style
Mykhaylyuk V, Sobchuk OV. Baire classification of discretely continuous functions and dependence on a countable number of coordinates. Bukovinian Mathematical Journal. 2018; 1(191).
Chicago/Turabian Style
Volodymyr Mykhaylyuk, Oleksandr Vasyliovych Sobchuk. 2018. "Baire classification of discretely continuous functions and dependence on a countable number of coordinates". Bukovinian Mathematical Journal. 1 no. 191.
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