On sets of points of approximate continuity and ϱ-upper continuity

Year, pages: 2020, 305 - 318

In the paper some properties of sets of points of approximate continuity and ϱ-upper continuity are presented. We will show that for every Lebesgue measurable set $E\subset \mathbb{R}$ there exists a function $f\colon\re\to\re$ which is approximately ϱ-upper continuous exactly at points from $E$. We also study properties of sets of points at which real function has Denjoy property. Some other related topics are discussed.

Kamińska, A., Nowakowska, K., Turowska, M. 2020. On sets of points of approximate continuity and ϱ-upper continuity. In Mathematica Slovaca, vol. 70, no.2, pp. 305-318. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0353

Kamińska, A., Nowakowska, K., Turowska, M. (2020). On sets of points of approximate continuity and ϱ-upper continuity. Mathematica Slovaca, 70(2), 305-318. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0353

Publisher: Mathematical Institute, Slovak Academy of Sciences, Bratislava