Separately continuous functions with respect to a variable frame

• Datum: 2004
• Hauptverfasser: Herasymchuk, V. H., Maslyuchenko, V. K., Maslyuchenko, O. V., Герасимчук, В. Г., Маслюченко, В. К., Маслюченко, О. В.
• Format: Artikel
• Sprache: Ukrainisch; Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2004
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/3841
• Назва журналу: 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...