Том 71
№ 4

All Issues

Herasymchuk V. H.

Articles: 1
Brief Communications (Ukrainian)

Separately continuous functions with respect to a variable frame

Herasymchuk V. H., Maslyuchenko O. V., Maslyuchenko V. K.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2004. - 56, № 9. - pp. 1281-1286

We show that the set D(f) of discontinuity points of a function f : R 2R 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.