On the sums of functions satisfying the condition (s1).

Abstract

A function $f:{\mathR} \to {\mathR}$ satisfies the condition $(s_1)$ if for each real $r > 0$, for each $x$, and for each set $U \ni x$ belonging to the density topology there is an open interval $I$ such that $C(f) \supset I \cap U \neq \emptyset $ and $f(U\cap I) \subset (f(x)-r,f(x)+r)$. ($C(f)$ denotes the set of all continuity points of $f$). In this article we investigate the sums of two Darboux functions satisfying the condition $(s_1)$.