Some properties of strongly differentiable continuous functions on products

Karlova Olena

Karlova Olena ^1,2

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

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

Keywords: distinctly continuous functions

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Abstract

We investigate strongly separately continuous function on subsets of products of topological spaces. We prove that the class of all strongly separately continuous functions is closed under sums, differences, products, uniform limits and locally finite limits, but is not closed under quotients. Moreover, we investigate determining sets in the class of strongly separately continuous functions.

References

[1] J. Činčura, T. Šalát and T. Visnyai, On separately continuous functions $f: \mathcal{l}^2 → \mathbb{R},$ Acta Acad. Paedagog. Agriensis, XXXI (2004), 11–18.

[2] O. Dzagnidze, Separately continuous function in a new sense are continuous , Real Anal. Exchange 2 (1998-99), 695–702.

[3] W. Sierpiński, Sur une propertie de fonctions de deux variables réeles, continuous par rapport à chacune de variables , Publ. Mat. Univ. Belgrade, vol.1 (1932), 125–128.

[4] T. Visnyai, Strongly separately continuous and separately quasicontinuous functions $f: \mathcal{l}^2 → \mathbb{R},$ Real Anal. Exchange 38:2 (2013), 499–510.

[5] O. Karlova, On Baire classification of strongly separately continuous functions , Real Analysis Exchange.

[6] O. Karlova, V. Mykhaylyuk, On strongly separately continuous mappings on products , Math. Slovaca.

[7] O. Karlova, Strongly non-narrowly continuous functions and one characterization of open sets in the box product, Mat.

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ACS Style: Karlova, O. Some properties of strongly differentiable continuous functions on products. Bukovinian Mathematical Journal. 2016, 2
AMA Style: Karlova O. Some properties of strongly differentiable continuous functions on products. Bukovinian Mathematical Journal. 2016; 2(2-3).
Chicago/Turabian Style: Olena Karlova. 2016. "Some properties of strongly differentiable continuous functions on products". Bukovinian Mathematical Journal. 2 no. 2-3.

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