Real Analysis Exchange

Universally bad Darboux functions in the class of additive functions

Dariusz Banaszewski

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Abstract

The main result: For every family \(\mathcal{G}\) of additive functions with \(\text{card }{\mathcal{G}}=2^\omega\) if the covering of the family of all level sets of functions from \(\mathcal{G}\) is equal to \(2^\omega\), then there exists an additive Darboux function \(f\) such that \(f+g\) is Darboux for no \(g\in\mathcal{G}\).

Article information

Source
Real Anal. Exchange, Volume 22, Number 1 (1996), 284-291.

Dates
First available in Project Euclid: 1 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.rae/1338515221

Mathematical Reviews number (MathSciNet)
MR1433614

Zentralblatt MATH identifier
0879.26014

Subjects
Primary: 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) {For properties determined by Fourier coefficients, see 42A16; for those determined by approximation properties, see 41A25, 41A27}
Secondary: 26A51: Convexity, generalizations

Keywords
Darboux function additive function universally bad Darboux function maximal additive family

Citation

Banaszewski, Dariusz. Universally bad Darboux functions in the class of additive functions. Real Anal. Exchange 22 (1996), no. 1, 284--291. https://projecteuclid.org/euclid.rae/1338515221


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References

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