Gabriel Istrate. Sums of continuous and Darboux functions. Real Analysis Exchange, 20 (2), pp. 842846, 1995.
Abstract:
For interval I and set A, denote by D(I,A) the class of functions from I to R such that:
1. range(f) = A.
2. for every x in A, f^{1}(x) is dense in I.
Motivated by a result due to Natkaniec and Kircheim (Real Analysis Exchange vol. 16 /199192) we show that D(I,A) is a subset of C+D, the class of functions that are the sum of a continuous and a
Darboux function, if and only if set A is an interval.
A preliminary version (called "On a paper by Natkaniec and Kircheim") is available from Citeseer (cached PDF), at
http://citeseer.ist.psu.edu/120021.html
The paper is not yet available online in journal form (it may become so in the future). The URL listed below is that of Real Analysis Exchange on Project Euclid.
Keywords:
sums of Darboux and continuous functions, real analysis
URL:
http://projecteuclid.org/Dienst/UI/1.0/Journal?authority=euclid.rae
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Gabriel Istrate
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