×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: EuDML
References:
[1] BORSIK J.: Maxima and minima of simply continuous and quasicontinuous functions. Math. Slovaca 46 (1996), 261-268. · Zbl 0889.54005
[2] GRANDE Z.-NATKANIEC T.: Lattices generated by \(T\)-quasi-continuous functions. Bull. Polish Acad. Sci. Math. 34 (1986), 525-530. · Zbl 0623.26004
[3] KEMPISTY S. : Sur les fonctions quasicontinues. Fund. Math. 19 (1932), 184-197. · Zbl 0005.19802
[4] MALISZEWSKI A.: On the limits of strong Swiatkowski functions. Zeszyty Nauk. Politech. Lodz. Mat. 27 (1995), 87-93. · Zbl 0885.26002
[5] MALISZEWSKI A.: Maximums of Darboux quasi-continuous functions. Math. Slovaca 49 (1999), 381-386. · Zbl 0961.26003
[6] MALISZEWSKI A.: Maximums of almost continuous functions. · Zbl 1107.26007
[7] NATKANIEC T.: On the maximum and the minimum of quasi-continuous functions. Math. Slovaca 42 (1992), 103-110. · Zbl 0789.54021
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.