Separately continuous functions with respect to a variable frame

  • V. H. Herasymchuk
  • V. K. Maslyuchenko
  • O. V. Maslyuchenko


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.
How to Cite
Herasymchuk, V. H., V. K. Maslyuchenko, and O. V. Maslyuchenko. “Separately Continuous Functions With Respect to a Variable Frame”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, no. 9, Sept. 2004, pp. 1281-6,
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