Cauchy equation and countable sets. (Ecuaţia lui Cauchy şi mulţimi numărabile.) (Romanian. English summary)

Gaz. Mat., Ser. B 119, No. 11, 497-499 (2014).

Summary: We prove that the functions satisfying Cauchy’s functional equation outside a countable set $N\subset{\bbfR}$ can be obtained by redefining, in an arbitrary manner on $N$, the functions satisfying Cauchy’s functional equation everywhere on ${\bbfR}$.