Real Analysis Exchange

On Internally Strong Świątkowski Functions

Mariola Marciniak and Paulina Szczuka

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Abstract

In this paper we introduce some notions which are related to quasi-continuity and a strong Świątkowski property. We examine the basic properties, the uniform closure, and several varieties of maximal classes for the family of internally strong Świątkowski functions. Moreover we study when the function \(f\) can be expressed as the sum of two internally quasi-continuous functions and the sum of two internally strong Świątkowski functions.

Article information

Source
Real Anal. Exchange, Volume 38, Number 2 (2012), 259-272.

Dates
First available in Project Euclid: 27 June 2014

Permanent link to this document
https://projecteuclid.org/euclid.rae/1403894892

Mathematical Reviews number (MathSciNet)
MR3261877

Zentralblatt MATH identifier
1301.54033

Subjects
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

Keywords
Darboux function quasi-continuous function strong Swiatkowski function

Citation

Marciniak, Mariola; Szczuka, Paulina. On Internally Strong Świątkowski Functions. Real Anal. Exchange 38 (2012), no. 2, 259--272. https://projecteuclid.org/euclid.rae/1403894892


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