Some remarks on density-continuous functions (Q581686)

Density continuous functions, i.e. functions transforming R into R, which are continuous when both domain and range are equipped with the density topology has been studied mainly by K. Ostaszewski and later by L. Larson and K. Ciesielski. The paper under review answers some questions posed by Ostaszewski. Here are the main results: real-analytic functions are density continuous and there is a differentiable continuous function f with positive derivative such that \(f(x)+x\) is not density continuous at 0.