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2002-2003 On the sums of functions satisfying the condition (s1).
Zbigniew Grande
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Real Anal. Exchange 28(1): 41-54 (2002-2003).


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 $(s_1)$.


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Zbigniew Grande. "On the sums of functions satisfying the condition (s1).." Real Anal. Exchange 28 (1) 41 - 54, 2002-2003.


Published: 2002-2003
First available in Project Euclid: 12 June 2006

MathSciNet: MR1973967

Primary: 26A05 , 26A15

Keywords: condition $(s_1)$ , condition $(s_2)$ , continuity. , density topology

Rights: Copyright © 2002 Michigan State University Press

Vol.28 • No. 1 • 2002-2003
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