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Oscillations of differentiably continuous functions on the product of Eberlein compact sets
Maslyuchenko Oleksandr Volodymyrovych 1,2
1 Institute of Mathematics, University of Silesia in Katowice, Katowice, 40-007, Poland
2 Department of Mathematical Analysis, Yuriy Fedkovych Chernivtsi National University, Chernivtsi, 58000, Ukraine
Keywords: differentiably continuous functions, Eberlein compact
Abstract

It is constructed a separately continuous function on product of two Eberlein compact with given oscilation.

References

[1] Maslyuchenko V.K., Mykhailiuk V.V., Sobchuk O.V. Studies on distinctly continuous functions // Proceedings of the International Math. Conference in Memory of Hans Hahn – Chernivtsi: Ruta, 1995. – P.192–246.

[2] Mykhailiuk V.V. Characterization of sets of points of discontinuity of distinctly continuous functions on products of metrizable spaces // Ibid. – P.103.

[3] Maslyuchenko V.K., Maslyuchenko O.V. Construction of a distinctly continuous function with a given oscillation // Ukr. Math. Journal – 1998. – 50, No.7. – P.948–959.

[4] Maslyuchenko O.V. On the characterization of oscillations of discretely continuous functions // All-Ukrainian scientific conference "Development and application of mathematical models in scientific and technical research", dedicated to the 70th anniversary of the birth of Professor P.S. Kazimirsky (October 5-7, 1995): Abstracts of reports. Part 1. – Lviv, 1995. – p. 80–81.

[5] Arkhangelsky A.V. Topological spaces of functions. – M.: Publishing house of Moscow University, 1989.–222 p.

[6] Namioka I. Separate continuity and joint continuity // Pacif. J. Math. – 1974. – 51, N2. – P.515–531.

[7] Amir D., Lindenstraus J. The structure of weakly compact set in Banach spaces // Ann. of Math. – 1986. – 88. – C.35–46.

Cite
ACS Style
Maslyuchenko, O.V. Oscillations of differentiably continuous functions on the product of Eberlein compact sets. Bukovinian Mathematical Journal. 2018, 1
AMA Style
Maslyuchenko OV. Oscillations of differentiably continuous functions on the product of Eberlein compact sets. Bukovinian Mathematical Journal. 2018; 1(76).
Chicago/Turabian Style
Oleksandr Volodymyrovych Maslyuchenko. 2018. "Oscillations of differentiably continuous functions on the product of Eberlein compact sets". Bukovinian Mathematical Journal. 1 no. 76.
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