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 $(s_1)$.
Publié le : 2002-05-14
Classification:
Density topology,
condition $(s_1)$,
condition $(s_2)$,
continuity.,
26A05,
26A15
@article{1150118733,
author = {Grande, Zbigniew},
title = {On the sums of functions satisfying the condition (s<sub>1</sub>).},
journal = {Real Anal. Exchange},
volume = {28},
number = {1},
year = {2002},
pages = { 41-54},
language = {en},
url = {http://dml.mathdoc.fr/item/1150118733}
}
Grande, Zbigniew. On the sums of functions satisfying the condition (s1).. Real Anal. Exchange, Tome 28 (2002) no. 1, pp. 41-54. http://gdmltest.u-ga.fr/item/1150118733/