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Comparison of some families of real functions in porosity terms

  • Małgorzata Filipczak EMAIL logo , Gertruda Ivanova and Julia Wódka
Published/Copyright: September 22, 2017
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 67 Issue 5

Abstract

We consider the following families of real-valued functions: Darboux, quasi-continuous, Świątkowski functions and strong Świątkowski functions. The aim of this paper is to compare this sets in terms of topology.

MSC 2010: Primary 26A15; Secondary 54C50
Keywords: porosity; quasi-continuous function; Darboux function; Świątkowski and strong Świątkowski function

Communicated by Ján Borsík

References

[1] Bruckner, A. M.—Ceder, J. C.: Darboux continuity, Jahresber. Deutsch. Math. Ver. 67 (1965), 93–117.Search in Google Scholar

[2] Dolzenko, E. P.: Boundary properties of arbitrary functions, Izvestija Akad Nauk SSSR, Ser. mat. 31 (1967)(in Russian), 3–14.10.1070/IM1967v001n01ABEH000543Search in Google Scholar

[3] Grande, Z.: On a subclass of the family of Darboux functions, Colloq. Math. 117 (2009), 95–104.10.4064/cm117-1-6Search in Google Scholar

[4] Ivanova, G.—Wagner-Bojakowska, E.: On some modification of Darboux property, Math. Slovaca 66 (2016), 79–89.10.1515/ms-2015-0117Search in Google Scholar

[5] Kempisty, S.: Sur les fonctions quasicontinues, Fund. Math. 19 (1932), 184–197.10.4064/fm-19-1-184-197Search in Google Scholar

[6] Kucner, J.: Funkcje Posiadające Silną Własność Świątkowskiego, Phd thesis, Łódź. 2002.Search in Google Scholar

[7] Kuratowski, K.—Sierpiński, W.: Sur un probleme de M. Fréchet concernant les dimensions des ensembles linéaires, Fund. Math. 8 (1926), 192–200.10.4064/fm-8-1-193-200Search in Google Scholar

[8] Maliszewski, A.: Darboux Property and Quasi-continuity. A Uniform Approach, WSP, Słupsk, 1996.Search in Google Scholar

[9] Maliszewski, A.: On the limits of strong Świą% tkowski functions. Zeszyty Nauk. Politech. Łódź. Mat. 27 (1995), 87–93.Search in Google Scholar

[10] Maliszewski, A.—Wódka, J.: Products of Świątkowski functions, Math. Slovaca 66 (2016), 601–604.10.1515/ms-2015-0163Search in Google Scholar

[11] Maliszewski, A.—Wódka, J.: Products of Świątkowski and quasi-continuous functions, J. Appl. Anal. 20 (2014), 129–132.10.1515/jaa-2014-0014Search in Google Scholar

[12] Mańk, T.—Świątkowski, T.: On some class of functions with Darboux’s characteristic, Zeszyty Nauk. Politech. Łódz. Mat. 11 (1977), 5–10.Search in Google Scholar

[13] Marcus, S.: Sur les fonctions quasicontinues au sens de S. Kempisty, Colloq. Math. 8 (1961), 47–53. http://matwbn.icm.edu.pl/ksiazki/fm/fm19/fm19115.pdf10.4064/cm-8-1-47-53Search in Google Scholar

[14] Pawlak, R. J.: Przekształcenia Darboux, dissertation, Łódź University, 1985, (in Polish).Search in Google Scholar

[15] Wódka, J.: Subsets of some families of real functions and their algebrability, Linear Algebra Appl. 459 (2014), 454–464, JCR.10.1016/j.laa.2014.07.015Search in Google Scholar

[16] Zajiček, L.: On σ-porous sets in abstract spaces, Abstr. Appl. Anal. 5 (2005), 509–534.10.1155/AAA.2005.509Search in Google Scholar

Received: 2015-6-30
Accepted: 2016-1-11
Published Online: 2017-9-22
Published in Print: 2017-10-26

© 2017 Mathematical Institute Slovak Academy of Sciences

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  2. Cyclic and rotational latin hybrid triple systems
  4. Notes on mildly distributive semilattices
  6. On generalized completely distributive posets
  8. Properties of non-associative MV-algebras
  10. On the upper and lower exponential density functions
  12. Quadratic permutations, complete mappings and mutually orthogonal latin squares
  14. On F-groups with the central factor of order p4
  16. Comparison of some families of real functions in porosity terms
  18. Negative interest rates: why and how?
  20. Homoclinic and heteroclinic motions in hybrid systems with impacts
  22. Some fixed point theorems in Branciari metric spaces
  24. S-essential spectra and measure of noncompactness
  26. Unified approach to graphs and metric spaces
  28. On structural properties of porouscontinuous functions
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  32. On The betti numbers of oriented Grassmannians and independent semi-invariants of binary forms
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https://doi.org/10.1515/ms-2017-0039
Keywords for this article
porosity; quasi-continuous function; Darboux function; Świątkowski and strong Świątkowski function

Articles in the same Issue

  2. Cyclic and rotational latin hybrid triple systems
  4. Notes on mildly distributive semilattices
  6. On generalized completely distributive posets
  8. Properties of non-associative MV-algebras
  10. On the upper and lower exponential density functions
  12. Quadratic permutations, complete mappings and mutually orthogonal latin squares
  14. On F-groups with the central factor of order p4
  16. Comparison of some families of real functions in porosity terms
  18. Negative interest rates: why and how?
  20. Homoclinic and heteroclinic motions in hybrid systems with impacts
  22. Some fixed point theorems in Branciari metric spaces
  24. S-essential spectra and measure of noncompactness
  26. Unified approach to graphs and metric spaces
  28. On structural properties of porouscontinuous functions
  30. A class of topological spaces between the classes of regular and urysohn spaces
  32. On The betti numbers of oriented Grassmannians and independent semi-invariants of binary forms
  34. Generalized Baskakov type operators
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