On sums of Darboux functions. (English) Zbl 0802.26003

Natkaniec, T.

Acta Univ. Carol., Math. Phys. 34, No. 2, 107-111 (1993).

In this paper the author investigates the following problem: Under what assumption on the family \(F\) of real functions of a real variable is one of the following conditions satisfied?
a(F): there exists a Darboux function \(g\) such that \(f+g\) is Darboux for each \(f \in F\),
c(F): there exists a Darboux function \(g\) such that \(f+g\) is Darboux for no \(f \in F\).

Reviewer: R.Pawlak (Łódź)

MSC:

26A15	Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable
54C40	Algebraic properties of function spaces in general topology

Keywords:

ideal; Darboux property in the Pawlak sense; Darboux function