The set of discontinuity points of quasicontinuous functions on Eberlein compact sets

Maslyuchenko Oleksandr Volodymyrovych; Onypa Denys Pavlovich

Maslyuchenko Oleksandr Volodymyrovych ^1,2 , Onypa Denys Pavlovich 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: quasicontinuous functions, Eberlein compact

Download

Abstract

We prove that every separable $F_σ$-subset of first category of an Eberlein’s compact is the discontinuity point set of some quasi-continuous function.

References

[1] Kershner R. The continuity of functions of many variables // Trans. Amer. Math. Soc. - 1943. - P.30-44.

[2] Breckenridge J.C., Nishiura T. Partial continuity, quasicontinuity and Baire spaces // Bull. Inst. Acad. Sinica. - 1976. - 4, N2. - P.191-203.

[3] Maslyuchenko V. K., Mikhailuk V. V. Characterization of sets of breakpoints of normally continuous functions of many variables on products of metric spaces // Ukrainian Mathematical Journal - 2000. - 52, N6. - p.740-747.

[4] Maslyuchenko O. V. Oscillations of non-negatively continuous functions on the product of Eberlein compacts // Scientific Bulletin of Chernivtsi University. Issue 76. Mathematics series. - 2000. - P.67-70.

[5] Maslyuchenko O. V. The discontinuity point sets of quasi-continuous functions // Bull. Australian Math. Soc. - 2007. - 75 . - P.373-379.

[6] Maslyuchenko O. V. The oscillation of quasicontinuous functions on pairwise attainable spaces // Houston Journal of Mathematics. 2009. - 35 , N1. - P.113-130.

[7] Amir D., Lindenstraus I. The structure of weakly compact sets in Banach spaces // Ann. Math. - 1968. - 88 , N1. - P.35-46.

Download

Cite

ACS Style: Maslyuchenko, O.V.; Onypa, D.P. The set of discontinuity points of quasicontinuous functions on Eberlein compact sets. Bukovinian Mathematical Journal. 2016, 1
AMA Style: Maslyuchenko OV, Onypa DP. The set of discontinuity points of quasicontinuous functions on Eberlein compact sets. Bukovinian Mathematical Journal. 2016; 1(1-2).
Chicago/Turabian Style: Oleksandr Volodymyrovych Maslyuchenko, Denys Pavlovich Onypa. 2016. "The set of discontinuity points of quasicontinuous functions on Eberlein compact sets". Bukovinian Mathematical Journal. 1 no. 1-2.

Export

BibTex EndNote RIS