Real Analysis Exchange

Maximal classes for the family of strong Światkowski functions.

Paulina Szczuka

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In this paper we introduce the class of extra strong \'Swi\c{a}tkowski functions, and we characterize the following maximal classes for the families of strong \'Swi\c{a}tkowski and extra strong \'Swi\c{a}tkowski functions: the maximal additive class, the maximal multiplicative class, and the maximal class with respect to maximums.

Article information

Real Anal. Exchange, Volume 28, Number 2 (2002), 429-438.

First available in Project Euclid: 20 July 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 26A21: Classification of real functions; Baire classification of sets and functions [See also 03E15, 28A05, 54C50, 54H05] 54C30: Real-valued functions [See also 26-XX]
Secondary: 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} 54C08: Weak and generalized continuity

Darboux function strong \'Swi\c{a}tkowski function extra strong \'Swi\c{a}t\-kow\-ski function.


Szczuka, Paulina. Maximal classes for the family of strong Światkowski functions. Real Anal. Exchange 28 (2002), no. 2, 429--438.

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  • A. Maliszewski, On the limits of strong Świątkowski functions, Zeszyty Nauk. Politech. \Lódz. Mat., 27 (1995), no. 719, 87–93.
  • A. Maliszewski, Maximums of almost continuous functions, in preparation.