There are many kinds of the generalization of continuity. T. Šalátraised the question: Can everywhere discontinuous solution of Cauchy functional equationf(x + y) = f(x) + f(y)be continuous in some generalized sense? The paper deals with this question.
@article{34, title = {Cauchy functional equation and generalized continuity}, journal = {Tatra Mountains Mathematical Publications}, volume = {43}, year = {2009}, doi = {10.2478/tatra.v44i0.34}, language = {EN}, url = {http://dml.mathdoc.fr/item/34} }
Kostyrko, Pavel. Cauchy functional equation and generalized continuity. Tatra Mountains Mathematical Publications, Tome 43 (2009) . doi : 10.2478/tatra.v44i0.34. http://gdmltest.u-ga.fr/item/34/