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Universally bad Darboux functions in the class of additive functions. (English) Zbl 0879.26014

Summary: The main result: For every family \(\mathcal G\) of additive functions with 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 \(g\in \mathcal G\).

MSC:

26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable