Separately continuous functions with respect to a variable frame

• Date: 2004
• Main Authors: Herasymchuk, V. H., Maslyuchenko, V. K., Maslyuchenko, O. V., Герасимчук, В. Г., Маслюченко, В. К., Маслюченко, О. В.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2004
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3841
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We show that the set D(f) of discontinuity points of a function f : R 2 → R continuous at every point p with respect to two variable linearly independent directions e 1(p) and e 2(p) is a set of the first category. Furthermore, if f is differentiable along one of directions, then D(f) is a nowhere d...