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Porosity and typical properties of real-valued continuous functions

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Summary

Some well-known theorems on typical properties of real-valued continuous functions defined on [0, 1] are improved using the notion of porosity.

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References

  1. S. Banach, Über die Bairesche Kategorie gewisser Funktionenmengen. Studia Math. 3 (1931), 174–179.

    MATH  Google Scholar 

  2. A. M. Bruckner, Differentation of Real Functions, L.N.M. 659, Berlin-Heidelberg-New York 1978.

  3. E. P. Dolženko, The boundary properties of arbitrary functions. Russian, Izv. Akad. Nauk. SSSR, Ser. Mat.31 (1967), 3–14.

    Google Scholar 

  4. V. Jarník, Über die Differenzierbarkeit stetiger Funktionen. Fund. Math.21 (1933), 48–58.

    Google Scholar 

  5. S. Mazurkiewicz, “Sur les fonctions non-dérivables”. Studia Math. 3 (1931), 92–94.

    MATH  Google Scholar 

  6. C. Neugebauer, A Theorem on derivatives. Acta Sci. Math. (Szeged)23 (1962), 79–81.

    MATH  MathSciNet  Google Scholar 

  7. L. Zají Ček, Sets of cr-porosity and sets of σ-porosity (q). Casopis Pest. Mat. 101 (1976).

  8. T. Zamfirescu, How many sets are porous? Proc. Amer. Math. Soc.100 (1987), 383–387.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Matematica, Via Carlo Alberto 10, Università, 10135, Torino, Italy

    P. M. Gandini & A. Zucco

Authors
  1. P. M. Gandini
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  2. A. Zucco
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Gandini, P.M., Zucco, A. Porosity and typical properties of real-valued continuous functions. Abh.Math.Semin.Univ.Hambg. 59, 15–21 (1989). https://doi.org/10.1007/BF02942311

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  • DOI: https://doi.org/10.1007/BF02942311

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