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On the discrete ideal convergence of sequences of quasi-continuous functions

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Abstract

For any Borel ideal \({\mathcal{I}}\) we describe the discrete \({\mathcal{I}}\)-Baire system generated by the family of quasi-continuous real-valued functions. We characterize Borel ideals \({\mathcal{I}}\) for which ideal and ordinary discrete Baire systems coincide.

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References

  1. J. Borsík, Algebraic structures generated by real quasicontinuous functions, Tatra Mt. Math. Publ., 8 (1996), 175–184; Real functions ’94 (Liptovský Ján, 1994).

  2. Bouziad A., Troallic J.-P.: Lower quasicontinuity, joint continuity and related concepts. Topology Appl. 157, 2889–2894 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  3. Császár Á., Laczkovich M.: Discrete and equal convergence. Studia Sci. Math. Hungar. 10, 463–472 (1975)

    MathSciNet  MATH  Google Scholar 

  4. Debs G., Saint Raymond J.: Filter descriptive classes of Borel functions. Fund. Math. 204, 189–213 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  5. R. Filipów, T. Natkaniec and P. Szuca, Ideal convergence, in: Traditional and Present-day Topics in Real Analysis, dedicated to Professor Jan Stanisław Lipiński, Łódź University Press (Łódź, 2013), pp. 69–91.

  6. Filipów R., Szuca P.: Three kinds of convergence and the associated \({\mathcal{I}}\)-Baire classes. J. Math. Anal. Appl. 391, 1–9 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  7. Grande Z.: Sur la quasi-continuité et la quasi-continuité approximative. Fund. Math. 129, 167–172 (1988)

    MathSciNet  MATH  Google Scholar 

  8. Grande Z.: On discrete limits of sequences of approximately continuous functions and T ae-continuous functions. Acta Math. Hungar. 92, 39–50 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  9. T. Jech, Set Theory, Springer Monographs in Mathematics, Springer-Verlag (Berlin, 2003). The third millennium edition, revised and expanded.

  10. Kempisty S.: Sur les fonctions quasicontinues. Fund. Math. 19, 184–197 (1932)

    MATH  Google Scholar 

  11. C. Kuratowski, Topologie, Vol. I, Monografie Matematyczne, Tom. 20, Państwowe Wydawnictwo Naukowe (Warsaw, 1958), 4ème éd.

  12. Kwela A.: A note on a new ideal. J. Math. Anal. Appl. 430, 932–949 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  13. Laczkovich M., Recław I.: Ideal limits of sequences of continuous functions. Fund. Math. 203, 39–46 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  14. C. Laflamme, Filter games and combinatorial properties of strategies, in: Set theory (Boise, ID, 1992–1994), Contemp. Math. 192, Amer. Math. Soc. (Providence, RI, 1996), pp. 51–67.

  15. A. Maliszewski, Sums and products of quasi-continuous functions, Real Anal. Exchange, 21 (1995/96), 320–329.

  16. Natkaniec T., Szuca P.: On the ideal convergence of sequences of quasi-continuous functions. Fund. Math. 232, 269–280 (2016)

    MathSciNet  MATH  Google Scholar 

  17. C. Richter, Representing cliquish functions as quasiuniform limits of quasicontinuous functions, Real Anal. Exchange, 27 (2001/02), 209–221.

  18. J. Wesołowska, On sets of discrete convergence points of sequences of real functions, Real Anal. Exchange, 29 (2003/04), 107–120.

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Authors and Affiliations

  1. Institute of Mathematics, Faculty of Mathematics, Physics and Informatics, University of Gdańsk, 80-308, Gdańsk, Poland

    T. Natkaniec & P. Szuca

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  1. T. Natkaniec
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  2. P. Szuca
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Correspondence to P. Szuca.

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Natkaniec, T., Szuca, P. On the discrete ideal convergence of sequences of quasi-continuous functions. Acta Math. Hungar. 151, 69–81 (2017). https://doi.org/10.1007/s10474-016-0673-3

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  • DOI: https://doi.org/10.1007/s10474-016-0673-3

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