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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

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Volume 66, Issue 3


Compositions of ϱ-upper continuous functions

Stanisław Kowalczyk
Published Online: 2016-08-17 | DOI: https://doi.org/10.1515/ms-2015-0162


In the paper some properties of compositions of ϱ-upper continuous functions are presented. We will show conditions for a function f: II under which gf is ϱ-upper continuous for each ϱ-upper continuous function g: I → ℝ. A small generalization of Luzin-Menchoff Theorem and Zahorski Theorem will be discussed.

MSC 2010: Primary 26A15, 54C30

Keywords: approximately continuous functions; ϱ-upper continuous functions; Zahorski Theorem


  • [1]

    Borsík, J.: Some classes of strongly quasicontinuous functions, Real Anal. Exchange 30 (2004-05), 689–702.Google Scholar

  • [2]

    Bruckner, A. M.: Differentiation of Real Functions. Lecture Notes in Math., Springer-Verlag, Berlin-Heidelberg-New York, 1978.Google Scholar

  • [3]

    Karasińska, A.—Wagner-Bojakowska, E.: Some remarks on ϱ-upper continuous functions, Tatra Mt. Math. Publ. 46 (2010), 85–89.Google Scholar

  • [4]

    Kowalczyk, S.—Nowakowska, K.: A note on ϱ-upper continuous functions, Tatra Mt. Math. Publ. 44 (2009), 153–158.Google Scholar

  • [5]

    Kowalczyk, S.—Nowakowska, K.: Maximal classes for ϱ-upper continuous functions, J. Appl. Anal. 19 (2013), 69–89.Google Scholar

  • [6]

    Kowalczyk, S.—Nowakowska, K.: Maximal classes for the family of [λ, ϱ]-continuous functions, Real Anal. Exchange 36 (2010-11), 307–324.Google Scholar

  • [7]

    Ostaszewski, K.: Continuity in the Density Topology, Real Anal. Exchange 7 (1981-82), 259–269.Google Scholar

About the article

Received: 2012-12-17

Accepted: 2013-08-06

Published Online: 2016-08-17

Published in Print: 2016-06-01

Citation Information: Mathematica Slovaca, Volume 66, Issue 3, Pages 585–600, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2015-0162.

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