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Maximums of strong Świątkowski functions. (English) Zbl 1030.26003
The paper deals with so-called strong Świątkowski functions. Let \(I\) be an interval and \(f \: I \to \mathbb R\), where \(\mathbb R\) stands for the set of real numbers. \(f\) is called a strong Świątkowski function, if whenever \(a, b \in I, a < b\) and \(y \in (f(a),f(b))\), there is an \(x_0\) in \((a,b)\) such that \(f\) is continuous at \(x_0\) and \(f(x_0) = y\).
Characterizations are given of both the family of the maxima of strong Świątkowski functions and the lattice generated by the family of all strong Świątkowski functions.

26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable
54C30 Real-valued functions in general topology
26A21 Classification of real functions; Baire classification of sets and functions
54C08 Weak and generalized continuity
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