Separately continuous functions with respect to a variable frame
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 dense set.
English version (Springer): Ukrainian Mathematical Journal 56 (2004), no. 9, pp 1526-1531.
Citation Example: Herasymchuk V. H., Maslyuchenko O. V., Maslyuchenko V. K. Separately continuous functions with respect to a variable frame // Ukr. Mat. Zh. - 2004. - 56, № 9. - pp. 1281-1286.