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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.

##### MSC:
 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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